Picture provided by Kingdom Hearts II, which makes the trope a game mechanic. In particularly tough boss battles, when Sora is defeated there's a chance King Mickey will suddenly arrive to save him, fighting the boss in his place to charge up an energy meter, reviving Sora to fight again when it fills completely. The chance for it to happen at all is random, but it's possible to even have it happen multiple times in the same fight.
In Kingdom Hearts: Chain of Memories, Sora is alone facing Larxene (having angrily told Donald and Goofy to stay behind after they started questioning his trust in his memories), badly wounded after his fight with the Riku Replica. Just as she is about to attack him, Goofy's shield comes flying at her face, a spell heals Sora, and Goofy and Donald place themselves between Sora and Larxene, reminding Sora that they had promised to protect him and that they would always stick together. Cue asskicking.
The climax of Kingdom Hearts Dream Drop Distance has this happen three times in a row. Young Xehanort and Riku are squaring off over Sora's comatose body, with more time-traveling Xehanorts appearing around them. True to form, Mickey shows up and freezes the bad guys with a Stop spell - except Master Xehanort pulls a Villain Override on his younger self and has an all-out brawl with Riku. When Mickey's spell runs out, Lea shows up to stop Xehanort from possessing Sora. Before the heroes can escape, the Guardian grabs Riku and Mickey and tries to crush them...only to get squashed when Donald and Goofy teleport in using a star shard. Whew.
The beginning of Star Fox 64 features a Big Damn Heroes moment. The Star Fox team flies in and save Corneria from the invading forces of Andross' army.
Wolf O' Donnell gets one in Star Fox Assault when he saves Fox McCloud from a group of Aparoids.
Peppy sort of gets one during the cutscene before the final mission of Star Fox Assault when he crashes the heavily damaged Great Fox through the barrier blocking the team from entering the lair of the Aparoid Queen.
Actually, Slippy is about the only really important character who never got one of these moments individually in the series, which is kind of fitting when you consider that Slippy is probably the least popular Star Fox team member with the fanbase by a sizeable margin.
Red Dead Redemption has this happen as a gameplay mechanic. A man is being held up by roadside banditos? BANGBANGBANG! A scarred, grizzled man on horseback just took out three of them shooting from the hip. A man's wife is being lynched for being black? Thwip! The rope just got shot out. BLAM! All the racists got their brains shot out by a man in a poncho, walking calmly over to help the poor woman, holstering his shotgun. Being attacked by wolves in the middle of the desert? 4 rifle shots later, they lie dead on the ground, the poor man free to go home. Be it rapists, cattle thieves or stage coach robbers, John Marston will show up in the nick of time to stop them and save your life, before bidding you good day and going off on his next adventure. Best Rockstar hero ever? Survey says, yes.
The player can also choose to ignore these and, in some cases, even decide to help out the bad guys instead.
Story-wise, there's John saving rebel leader Abraham Reyes from execution and later Reyes returning the favor when the Mexican Army decides to betray him.
Subverted and lampshaded in Disgaea 2, when Beauty Queen Etna, arrives just in time to save the heroes from being overrun by a neverending flood of zombies. She's actually downright annoyed that she's wound up arriving just in the nick of time, "like one of those 'heroes of justice' losers", and considers just letting the zombies finish you off before taking on the Big Bad - fortunately for you, the Big Bad is carrying the Villain Ball, and sics the Mooks on her instead of letting them finish you. Cue the explosions.
Played straight and lampshaded later in the game with Axel arriving with his flute to subdue the Rifle Demons (see the second page quote)
In Tales of Symphonia, before facing Yggdrasill in Welgaia, all of the members of the party besides Lloyd apparently sacrifice their lives (via being caught in various traps) so that Lloyd may continue onward to face Yggdrasill. Finally, Lloyd enters the chamber in which Yggdrasill is waiting for the completion of the transfer of Martel's soul to Colette's body. Yggdrasill is shocked and extremely angry that Lloyd managed to reach him, and moves to kill him — but then a fireball from above stops Yggdrasill in his tracks. What do you know, the rest of the party didn't die after all, and appeared just in time to save Lloyd!
Final Fantasy IV. After smiting the Calcobrina dolls, the group is confronted by Golbez, who promptly douses them with a paralyzing agent before summoning a Shadow Dragon to start killing them. Kain gets off lucky if he's in the air before the gas goes off and when the killing begins; Rosa and Yang are still screwed. Golbez happened to be hiding the Villain Ball in his robe at the time, as he takes a moment to bid Cecil farewell...a moment too long, as that's when a Mist Dragon erases Golbez' Shadow Dragon and Cecil's paralysis is lifted via Unicorn Horn before the real boss battle begins.
As it turns out she's really good at these because she does it again in Final Fantasy IV: Interlude in almost the exact same way she did during the battle with Golbez. Just as the fake Rydia is about to utterly obliterate the party with Bahamut, the real Rydia shows up and blasts the imposter and Bahamut with her Mist Dragon. After a brief intermission the battle begins a new, but this time it's more of a curb stomp battle since this time you'll likely be using the very same power you almost got obliterated with.
Final Fantasy IX has one during a cutscene in Disc 3. Eiko and Dagger (Garnet) are praying to summon Alexander and save Alexandria. The Big Bad decides this a bad idea, however, and proceeds to destroy Alexander, with Dagger and Eiko still on him. Cut to Zidane swooping in to save Dagger at the last second, and Dagger with tears in her eyes hugs him for being there. Aww..
Yuna is gettin' hitched to the Big Bad, Seymour, so the party comes charging in on an airship to crash the wedding, guns blazing, kicking physics to the curb—and all they do is get overwhelmed by the amount of guards there and ruin Yuna's plan to Send Seymour by giving him material to threaten her with—kill him and they die too. They all wind up arrested and imprisoned anyhow, though were it not for Yuna thinking on her feet, they'd be dead. Yuna herself manages to escape and then has to go into the dungeon and rescue them alone. So this is a vicious inversion of the Distressed Damsel too.
Played superstraight later, on Bikanel Island. When Tidus wakes up, he is attacked by a monstrously huge Zuu bird, which he must fight for a few turns on his own before Auron and Lulu turn up to help him out. Level grinding or abuse of Delay Attack can result in confusion, before Tidus defeats the beast before he is rescued.
Final Fantasy XIII has one in the city of Palumpolum. Lightning and Hope are surrounded by hundreds of PSICOM soldiers, with their commander reminding the soldiers how "l'Cie are not human." Just as Lightning's telling Hope to run for his life so she can pull a Heroic Sacrifice/You Shall Not Pass...a section of the nearby building explodes and Snow comes out swinging, punching out several soldiers near him, tossing a gun to new comrade Fang, and summoning Shiva to glaze the whole damn plaza over with ice which he proceeds to ride the Shiva-bike on as Fang rides shotgun. Badass. You can tell Snow doing this because he refers to himself specifically as a "Hero".
Later in Palumpolum, after Hope has forgiven Snow, Snow collapses from exhaustion and is almost immediately attacked by an enormous Sanctum war machine. Hope tries to take the thing on by himself, but it is almost impossible to destroy it. Once Hope is defeated, Lightning and Fang arrive and join the fight, with Hope revived.
During the cutscene between the Final Boss' two forms, Lightning, Snow, Sazh and Hope are all dead (or at least Cie'th), Fang is being tortured and resurrected by Orphan mercilessly, and all Vanille can do is stand around and watch. Suddenly, a massive blast of magic hits Orphan, and Fang's body (thrown from the blast) is caught by Snow, with Lightning, Sazh and Hope just behind him - readily forgiving her and asking her to stand with them and fight. Much badassery followed.
During the second trip through the Forsaken Fortress in The Legend of Zelda: The Wind Waker, Tetra pulls this twice - once to distract the Helmarock King and buy time to rescue the captives and again when Link is in Ganondorf's grasp...only for this attempt to fail and require another dramatic rescue.
A pretty ironic example, considering that she's the damsel and he's the hero. Well, she's an Action Girl after all.
It also happens in Twilight Princess, as Link gets confronted by a hoard of enemies in Hyrule castle, and suddenly BAM. Cavalry. Well, infantry, but same effect.
Happens in every case of the Ace Attorney series at some point. The prosecution appears to have won and Phoenix is ready to give up but then...OBJECTION! Someone comes in with new evidence to save the day. The last case in the second game ends up boiling down to stalling until the big damn hero arrives.
The third case of the first and third games where Detective Gumshoe pulls this outside of court. Gumshoe's failed attempt at this in the fourth case of second game, and Franziska's pick up save off of this at the very last second.
It's subverted in Ace Attorney Investigations 2, where Franziska von Karma bursts into the room in case 4, delivering the news that the victim died from her head wound, not her stab wounds. Franziska's not happy when Edgeworth tells her they proved that five minutes ago.
We go this far and Larry Butz's big save in game 1, case 4 is left out? That one is one of the more epic ones.
Gumshoe ends up saving Phoenix and Maya's lives just as much as the cases.
This trope occurs in Halo games several times, with Master Chief rescuing marines, or Johnson rescuing the chief. The third game directly references the Trope Namer, as a character called Sergeant Reynolds, played by Nathan Fillion, states, "Looks like we got here just in the nick of time. What's that make us?" Gamers everywhere immediately replied "Big Damn Heroes, sir!"
In fact, part of the ad campaign for Halo 3 was based around the beneficiaries of such moments reminiscing about the hero who saved them. You can see a couple of these ads here and here.
Cortana: "Admiral, tell your men to hold their positions. Reinforcements are on the spoke."
Admiral: "The entire fleet is engaged Cortana. With respect, what the hell sort of reinforcements have you got?"
Mission Log: "STOP DESTRUCTION OF HUMAN RACE...IN PROGRESS"
The Master Chief then proceeds to throw himself out of a rapidly decompressing launch bay on a space station into a pitched space battle in Earth orbit to directly assault a Covenant cruiser...alone
Master Chief's mere precense seems to inspire this, given the quote from Sgt. Banks in Halo2:
Sgt. Banks:"When I asked for reinforcements, I didn't think they'd send a SPARTAN."
The Subspace Emissary of Super Smash Bros. Brawl has Sonic showing up just in time to prevent the final boss Tabuu from releasing a super attack on everyone. Also Ness and Falco get their Big Damn Heroes moment.
Meta Knight manages to save Lucas and Red/Pokemon Trainer from falling to their deaths (or rather falling to their trophycation).
Link, Mario, Pit, Kirby, and Yoshi get one as well, leaping off a cliff to come to the aid of some of the other heroes who're fighting off the Primids.
Every character gets one of these at one point or another. Fox bursting out of the wreckage of his Arwing to save Diddy Kong, Captain Falcon using his signature move to take out a ROB who's just annihilated Cpt. Olimar's pikmin team, Ike destroying a Subspace Bomb being carried by the Ancient Minister, this list could earn its own separate page.
Fire Emblem does this in every game out in the US (probably every game, period), generally as reinforcement to the story's lord showing when they are in a really serious bind. However on easier difficulties this often leads to the reinforcements needing AMAZING projection as they aren't as leveled.
The first example of the lord getting to be the "Big Damn Hero" is in Fire Emblem 7 (released in the states as Fire Emblem). Florina (a supporter to the tutorial chapter's lord, Lyn) arrives to the main team of heroes to tell how her Lyn and the castle are under attack, naturally the main team of the game go to save them.
Second example is in Fire Emblem 10, right when Lucia is going to be executed by the rebellion, The Greil Mercenaries in PERFECT Big Damn Heroes form all show up. What's great is that in the cutscene for their arrival, each one arrives saving another member of the party from being attacked. So any time the villains attempt a counter strike, they are instantly taken down. Making it a string of Big Damn Hero moments. One of the best--if not the best--cutscenes in the game.
In Mega Man Battle Network 6 (6 being the last game) in the 3rd to last (the last 2 being past the point of no return) cutscreen in the game, the villans realize it is a better idea to take on the Kid Hero in the real world then in cyberspace, only one of these moments save Lan.
To be broader, Battle Network loves this trope such much that it has a Leitmotif for it.
Special mention goes to Protoman, who gets these moments all the time.
Laker from Super Robot Wars Original Generation actually plans this, he lets Elzam keep the Kurogane, and occasionally gives him mechs so he can have moments like these, and aid the Hagane, and Hiryuu Custom from the shadows. In Original Generation 02 the Hagane did this a lot in the early levels pissing off the Shirogane's captain Lee Injun, who was jealous of the Hagane.
Sanger Zonvolt seems incapable of entering a scene in any other method. These include, saving his former subordinate from Sanger's Evil Knockoff, using his signature move to kill an enemy outright in his first appearance in battle, and when fighting his Evil Knockoff, falling through the ceiling of a shelter designed to survive the end of the world, just in time to save the party.
Axel Almer and Alfimi both did this in OG Gaiden to play part in the Super Robot Wars MX prologue. When the Jetzt wrecked the Cry Wolves, and it got Foglia killed, Hugo fatally wounded and Albero is sure in to be their next victim, suddenly both of them arrive and attracted the Jetzt, giving Albero time to escape with Hugo.
An official Super Robot Wars Alpha 3 manga features a rather epic version of this. After the Big Bad is defeated, Son Ganlong appears to take advantage of the Alpha Numbers' weakened state and finish them once and for all. At that point all the Alphas who didn't return in 3 show up to support their friends and dispense an almighty smackdown.
In Super Robot Wars Compact, Londo Bell comes to the rescue of Judau and Seabook in "A New Strength" and "Inside the Winds of Light". Judau in the former mission and Seabook in the latter mission
In the first Z game Kira Yamato as usual often appears out of nowhere in the Freedom to help your guys out, provided they aren't allied with Zaft. If you take the route where you are, he appears out of nowhere....to attack you instead.
There's another one as early as Stage 6. The Joule Team is attempting to stop the dropping of Junius Seven when the Mineva shows up with the heroes. Near the end, Memetic Beasts show up and surround the Mineva and attack the ship. When things look bleak, who does show up but Great Mazinger, who delivers a heaping serving of Thunder Break onto them!
2nd Original Generations gives us a Doozy: After spending several missions with the vast majority of the Steel Dragon Battle Group ends up Trapped in Another World, the game shifts to a few missions with the New Aggressors squad, along with Hugo and Aqua and D's Joshua Radcliffe. They find themselves surrounded in the initial moves of the Guest invasion, caught alone in the middle of the South Pacific. Suddenly, half the enemy force just explodes. Cue the Hagane and Hiryu Kai, back home from La Gias.
In Call of Duty 4 you both play as the Big Damn Heroes in several missions and are blown up by a nuke because of it in one outstanding, badass instance and are saved by the Big Damn Russians in the very last mission, though Gaz and Griggs would probably have preferred it if they could have arrived a few moments earlier....
In Modern Warfare 2, General Sheperd does this to the horribly outnumbered and wounded 141 squad led by Ghost and Roach, personally wielding a .44 magnum to fend off the Russian hordes.
In Earth 2160 we have one example. 3rd mission of Lunar Corporation campaign - two main characters (one of which was wounded in bomb explosion) are about to be torn to shreds by enemy mech with FOUR gatling cannons when suddenly three LC hover tanks shows up and without problem destroy above-mentioned mech.
The same line occurs in Mass Effect 1 on Virmire, when you ride in to rescue the Salarian recon squad. They are less than impressed with your Bad Ass selves, wondering why the Council didn't send the army they asked for.
And speaking of Mass Effect 1, what about "It's the Alliance! Thank the Goddess!" One of the possible endings has the Alliance fleet arrive just in time to save the Council and its flagship, the Destiny Ascension.
There's also the moment when you have to save the quarian (Tali) from being assassinated.
Highlighted in Mass Effect 2, when Zaeed says of his loyalty mission "Get it out of the way so we can concentrate on being big goddamn heroes."
It's really all over the place in both games: Feros with the geth attack, Noveria with the breakout of the rachni, the Citadel itself with Saren's attack, the first time you encounter Tali in both games and her recruitment mission in the second, the Archangel recruitment mission, the assault on the Collector base (if you do it soon enough), saving the hostages from terrorists...there's a reason by the second game paragon Shepard is considered by everyone, including the bad guys, the Biggest Damn Hero in the galaxy.
Shepard's casual way of explaining why they're on Haestrom, saving Tali from a small army of Geth;
Shepard: I was in the neighbourhood... thought you might need a hand?
Mass Effect 3 also has plenty. Most of the time, your allies get their asses handed to them... until you arrive. Then your three-man squad quickly blows all the enemies away. Also happens in a cutscene during the attempt by Cerberus to take the Citadel, but only if Thane survived the previous game. Just as Kai Leng is about to kill the Salarian Councilor, we see a gunbarrel at the back of his head. It's Thane! He manages to hold off the highly-skilled assassin for a bit, despite living on borrowed time. Then again, who else to stop an assassin but another assassin?
The third game's Citadel DLC has a truly glorious BDH moment. Shepard (unarmored and injured) and his/her Love Interest are pinned by a shuttle full of armed mercenaries (including a Geth Spitfire). Just when things look bad, Urdnot Wrex (or James Vega, if Wrex is dead or hates you) comes crashing through the window a floor above with a war cry, and crushes/elbow-drops the shuttle hard enough to force it down onto the landing pad. He then leaps into the shuttle and starts beating the crap out of the very surprised mooks with his bare fists (and his armor-plated head), knocking them senseless and tossing some of them out the doors and over the edge.
Earlier, you come up against a couple of CAT-6 mercs while your health is down to 20%, you're not wearing any armour, and there's no real cover. Your LI - or Liara, if you're romancing someone who was Demoted to Extra (Jack, Miranda, Thane) or was a Mauve Shirt from the get-go (Traynor, Cortez, Kelly), or if you just haven't locked in your main-game romance yet - will show up and take them out in about three seconds with biotics, tech attacks, or good old-fashioned bullets. They will then be distracted by your butt.
Really, by the third game, you have to wonder if the Alliance standing orders for the Normandy aren't just;
In Metal Gear Solid 4, Johnny Sasaki, the resident Butt Monkey of the series, saves both Solid "Old" Snake and Meryl in the Middle East and Eastern Europe, and then saves Meryl near the end of the game. Johnny and Meryl then proceed to kick a lot of ass, becoming a Battle Couple in the process. Also Raiden, who would save Snake's life at least twice...the first time cutting off an arm to do so, then the second time appearing without his arms, his sword (Rule of Cool) first clutched in his teeth and then in his left foot.
And followed up by Henry during the final boss of the sequel.
Subverted multiple times in Metroid Prime 3: Corruption, wherein the bounty hunters show up just in time to reactivate a dead orbital cannon and nuke the Space Pirates' asteroid weapon - and then just before they can hit the Big Red Button, Dark Samus shows up and blows them all away, achieving a Big Damn Villain moment of her own.
And then subverted yet again, as Samus turns out to be Only Mostly Dead, hauling herself to the control panel and activating the cannon before lapsing into a month-long Convenient Coma.
This is perhaps the only recorded case where this trope is well and truly inverted.
Samus pulls this off herself in Echoes, if you look at things from the point of view of the Luminoth. The Ing were two rooms away from accomplishing their dominations. Two rooms. Then Samus turns up.
Probably the most classic example of the series takes place in Super Metroid. Mother Brain has gone One-Winged Angel and is beating the crap out of Samus who, by the end, can't even stand up. Right as Mother Brain is about to deliver the final blow, the baby Metroid that Samus sort of adopted comes in and drains a massive amount of energy from Mother Brain and transfers it, and the Hyper Beam, to Samus. After that, it sacrifices itself in order to give Samus time to recover and finish Mother Brain off once and for all.
The World Ends with You has Neku and Shiki, in the third day, almost out of time. Then at the last second, Beat and Rhyme show up and finish off the "master of A-East." Since only one player needs to complete the mission to spare everyone from the threat of erasure that comes with running out of time, their action not only spared them, but also Neku, Shiki, and all the other players currently in the game.
Near the end of their week, Neku and Josh get a few chances to do this during a Taboo Noise rampage, two out of three of which you can skip over and the third one, oddly enough, forces you to save someone who is as good as dead even if you save him from the things.
At the beginning of the third week, Neku is the only player in the game after all the other players have been taken as his entry fee, meaning that he can't partner up with anybody and is completely defenseless. Just as he's about to get erased, Reaper Beat comes out of nowhere to form a pact with Neku.
In Mega Man X2, if X succeeds in retrieving all of Zero's parts from the X-Hunters, Zero will break into the Central Computer's core just before Sigma unleashes his Copy-Zero on X, then proceed to destroy the Copy himself and punch a hole in the floor for X to pursue Sigma, all accompanied by kick-ass heroic music.
At the end of Mega Man X3 either Zero or Dr. Doppler will arrive just in time to save X from the invincible Viral Sigma.
Mega Man X8 allows players to make a team of two characters to take on every level. In the last level in Hard Mode, however, one of them will be incapacitated by Vile going kamikaze. Later in the level, during the confrontation against Sigma, he gets the upper hand, and has the player in a choke hold (in a cutscene). Cue the other character swooping in to save his partner, and the battle resumes.
X returns the favor at the end of Mega Man Zero 3 when he and the three Guardians help Zero in defeating Omega once and for all.
But subverted in both Zero 2 and 4. In 2 you arrive to confront Elpizo, and he hasn't destroyed X yet. But as Zero dashes in, he's caught in a capture field and can only watch as X is destroyed. And in 4 Craft fires Ragnarok just as you reach the boss door.
At the beginning of Zero 4, the Caravan of humans that are fleeing from Neo Arcadia are being chased by Weil's forces, and just as the mooks descend on the Caravan, Zero arrives to save the day.
Earlier than that, when Marcus, Dom, and Rook- I mean Carmine are exploring the ruins of Ilima City and get pinned down by a squad of Locust, Cole pulls off a superb Big Damn Heroes by showing up and taking out the entire enemy squad by himself. "Nobody plays this game like me!", indeed.
Early on in Suikoden II, Flik and Victor show up just in time to stop the executions of the main character and Jowy. On your way out, you discover the main character's sister has broken out of jail on her own, and was on her way to attempt the same.
A variation in War Craft III. Arthas and the village have held the line as best they can, but finally the undead are proving unstoppable...and then Uther, with The Cavalry at his back, charges into battle. But despite his initial joy:
Arthas: Uther! Your timing couldn't have been better!
...he becomes defensive later, when he misinterprets Uther's admiration as disbelief that he was good enough to hold out so long.
In Half-Life 2: Episode 2, you try to protect a completely occupied vortigaunt and its barely-alive patient with two mauve-shirts and two busted turrets. By the last wave, it's the three of you and one working turret against dozens of Antlions. Then the last turret breaks down. You figure this is going to get unpleasant. Then, three Vortigaunts, who have been nothing but background filler until now, wander into the scene. Moments later, it's you, two mooks, and three Vortigaunts, against HUNDREDS of Antlions, all coming at once. And you know what? The Antlions never stood a chance.
Griggs said it best:
Griggs: Jesus! I've never seen the Vorts this PISSED!
Alyx gets a fine moment of her own in Half-Life 2 when she saves Gordon from the Metrocops early in the game. Then there's Gordon himself, who only hesitates to fling himself into alien dimensions and unstable fusion reactors if you, the player, make him.
It's made even more awesome when you hear snapping and the high-pitched whine from dead Metrocops.
And it decisively shifted the Vortigaunt's personality from fugly alien Magic Negros to definite badasses.
Half-Life 2 had its fair share of Big Damn Heroes moments like right before the climax of the game when Dog kills a squad of Combine soldiers using an APC as a weapon then goes flying through the air wrestling a Combine Dropship.
Tales of Phantasia offers a rather interesting example, wherein one character performs a Big Damn Heroes moment for the player characters...who immediately perform one back. Near the beginning of the game, the Big Bad Dhaos is unsealed, and Morrison casts a spell to send Cless and Mint 100 years into the past in order to save them from Dhaos. The two of them go on a journey (collecting two other allies in the process), and eventually activate another time warp to appear between Morrison and Dhaos, mere seconds after Morrison had sent them away. To the player, it took 30 or so hours of gameplay, but to the mentor and the bad guy, they appeared to have warped right back...until they proceed to kick Dhaos's ass, something they certainly couldn't have done when Dhaos first appeared.
In the fangame Mother: Cognitive Dissonance, you get two moments of this: When Alinivar's party is about to face off against the Greyface in the Pigmask recruitment center, both Niiue and Larice, the latter thought to be dead by the Greyface, burst into the room to help with the battle. Then when you start heading towards the end to defeat Giegue in the center of his mind as he becomes Giygas, two Niiues appear to keep your party topped on health and force Giegue to retreat further into himself in the Maelstrom.
In MOTHER 3, the end of chapter 3 has the party cornered by Fassad and his mob of Pigmask soldiers and tanks. They get a little worried after they manage to destroy one of the tanks, but it's not enough to make them back off. Cue Lucas showing up with his baby Drago friend, who promptly gets mocked, only to callits mother who proceeds to send the lot of them packing.
As a nod to the first Earthbound example, DCMC shows up to take out the remainder of the mob of Porky bots you fight near the end of the game once you've destroyed enough of them.
City of Heroes: Most of the missions involve you arriving just in time to save someone, keep something from being from being destroyed, or stop a villain's plan. The Trope Namer is actually referenced in one Task Force. The badge you get for defending the city's dam from three different groups of enemies is Big Dam Hero.
There's two in fairly close succession at the beginning of Valkyria Chronicles, the first where Welkin saves his adopted sisters life by clubbing an imperial soldier about to shoot her with a fence-post, the second moments later when the siblings get their dad's old tank up and running and perform a proper rescue of the town watch in Bruhl. Alicia even mentions 'Now you're my hero' to Welkin afterwards.
Lancer of Fate/stay night is king of this trope in the UBW path. Has his heart impaled, and then he kills the Big Bad of the last route in one attack. That's cool right? Heroic determination and stuff, nice from a guy who was just a minion. Only then Shinji shows up, and gets big damn heroed out as well, though not fatally. Still walking around and chatting sans heart, he lets Tohsaka go and burns the entire castle down.
Gilgamesh subverts it by turning into the next baddie. Archer zigzags on the 'hero' bit.
Rider does an unexpected one in Heaven's Feel, showing she's not as weak as she was in other routes.
Tragically subverted in Cave Story, wherein the BDH arrives moments too late to save the victim from being force fed a red flower, and is killed moments later when he tries to attack the villains in a rage. And then you have to Shoot the Dog.
Later played straight in the final, good ending, where you and Curly Brace are nearly crushed to death by a set of moving walls before Balrog the flying toaster, of all people, swoops in to save you.
In the last mission of Battalion Wars 2, Pierce has no fewer than 3 Big Damn Heroes moments: providing 3 Fighters to combat the air force; shooting down Kaiser Vlad's escape transport, rendering his obtaining the staff useless, at least until the next game; and giving Betty a ride on his personal Fighter to rescue her from being nuked by Vlad's usage of the staff used to call the satellite weapon.
MechWarrior 3, you have picked up two of your 3 available npc allies and are traveling across country to try and rendezvous with mechwarrior Keith Andrew, who you have been in contact with for much of the game. On the way, in dire need of repairs, you come across an enemy fortress and secure it for supplies. The enemy responds by sending a massive force, and another from the other way, and there's an assault mech closing from the west, wait isn't that...
Alan Matilla: Can you read me, Damocles Command? Looks like you need a hand.
Turns out you're also his best chance of survival since he can't even reload without assistance, but credit for the entrance. Keith Andrew never joins you and eventually meets with a rescue ship that you can't reach.
In MechWarrior 4: Mercenaries, the player can be this to the beleaguered 'Mechs of Hammer Lance, rushing in just in the nick of time to prevent them from being swarmed and annihilated by superior forces. If Hammer Lance survives, they will return the favor in kind during a later mission, one where you will be on your own against many enemies...and just to make it worse, it's also an Escort Mission besides.
In another mission, Spectre and his team come in as the Big Damn Reinforcements for one of the most pitched battles of the early storyline, Barlow Gap. Its defenders are badly outnumbered, outgunned, and outmassed, and are verbally confirmed to be moments from suffering numerous losses. One more assault almost costs the defense forces the strategic pass...until the Battlemechs of Spectre Lance appear to even the odds.
There's a great one of these in World of Warcraft, during the Northrend quest Tirion's Gambit.At the end of a long (and excellent) quest chain, you enlist the help of Tirion Fordring to get a shot at destroying an artifact important to the Lich King. You, Tirion and a small band of Argent Crusade paladins sneak incognito into the Cathedral of Darkness, but the Lich King appears and exposes you all. Surrounded by elite Cultists, you and the Crusaders prepare for a hopeless battle, when...
Koltira Deathweaver: Take courage, crusaders. You do not fight alone!
Highlord Darion Mograine and the Knights of the Ebon Blade rush in to save the day.
And now there is a new one with the Halls of Reflection instance. You attempt to confront the Lich King, but your group can't last, so you flee down a secret exit trying to hold off the hordes of approaching undead.
Trapped on the edge of a cliff outside the tunnel, Lich King closes in, and then your factions airship rises up the cliff behind you and seals the enemies in the tunnel with a few well aimed cannon blasts.
Horde players starting off in the Borean Tundra Northrend get their butts saved from the Scourge—or more directly, becoming a part of it—by none other than Varok Saurfang himself.
Alliance players have something similar happen during their version of the quest chain leading up to Wrathgate in Dragonblight. As the player is confronting the lich who is commanding the Scourge ground forces in the area, the lich simply casts a spell that paralyzes the player and all of the NPC Alliance soldiers who are present. As the lich is gloating about his seemingly easy victory, Bolvar Fordragon shows up and instantly frees everybody from the paralysis spell. Although the player can help in the ensuing battle, their contributions don't really amount to much as Bolvar more or less solos the aforementioned lich by himself.
Icecrown Citadel makes Tirion Fordring one. You think you're doing just fine, beating Arthas to pulp, but then, he just wipes the raid in an instant. Cue Fordring getting out of his ice block saving the day.
In the post-Cataclysm Eastern Plaguelands, there's a quest chain where you travel the Plaguelands with a caravan consisting of a merchant, two would-be Paladins, and others. When one of the would-be Paladins runs off and gets himself captured, it becomes your job to track him down and, upon doing so, you see a cutscene where everyone you recruited into the Caravan at that point will show up for the rescue.
In Mists of Pandaria, after completing the two areas Valley of the Four Winds and Krasarang Wilds, the great wall holding back the insectoid Mantid is broken and they begin to swarm a village in the valley. Chen Stormstout arrives to give a speech about defending their homes, and soon afterwards nearly every major NPC from both zones march down the hillside.
In Resident Evil 3: Nemesis, If Nicholai gets away with the helicopter (or you destroy it), Barry shows up with a helicopter and saves Jill and Carlos just before the nuke hits.
Later on, in Resident Evil 5, Chris and Sheva are being attacked by Ganados on dirt-bikes, and are just abrely holding them off - until Captain Stone and Delta Squad arrive to save the day in a thoroughly badass instance.
Subverted all the time in Final Fantasy Tactics: Ramza tries to storm the castle he thinks Princess Ovelia is held in, except he runs into Agrias, who managed to escape by herself; a subsequent rescue attempt turns out to be a trap. Throughout the plot, Ramza either stumbles into rescue missions by accident or arrives too late to do anything.
Depending on how much Level Grinding you did prior to fighting Wiegraf, the moment when your allies show up to reinforce you in the second stage of the battle, followed by Weigraf summoning his own monsters to even the score can be either a "awesome, cue the overkill" or Oh Crap moment.
Ace Combat 6, Mission 12: The Player Character and his Wingman saved their hometown from a WMD attack, and must now make it back to base. However, the Estovakians start to send in entire fighter squadrons (including a jammer and 2 AWACS in) to kill you. Just when you think you're about to die, cue every friend you ever helped to come and save your rear.
In Golden Sun 2, at the top of Jupiter lighthouse. Felix is initially ordered to move to the top of the lighthouse alone while the other party members try to help rescue the previous game's lead party. Piers insists on accompanying him, and the two are attacked by the 2 antagonists, Agatio and Karst, who had set the trap which detained the other characters. One by one the battle is interrupted as your party members return, and (just too late) eventually the entire cast of protagonists arrive, causing Agatio and Karst to retreat due to being outnumbered.
In Mario Party DS, after the shrunken heroes have a few rounds of "fun" in Bowser's pinball machine, he decides to use his rod to shrink them even further. Cue Donkey Kong bursting into the castle, disarming Bowser, and stomping on the rod, restoring everyone to normal. By accident.
At the end of the first BioShock, at the end of the fight against Fontaine, the spliced-up musclehead slams Jack across the room, stalks over, and is about to pound him/you into mush, when a Little Sister jumps on Fontaine from behind and stabs him with the ADAM-collecting syringe. After he throws her off, a small horde of Little Sisters jumps him and stab him to death.
Not the first time they do this - Tenenbaum sends them to help Jack escape after Fontaine takes over and sends security bots after him, and later guns down a Splicer who was after one of the Little Sisters.
Subverted when Sinclair tries to rescue Subject Delta - this only gets him captured by Splicers and turned into an Alpha Series Big Daddy for his troubles.
In Justice League Heroes, Superman is completely focused on breaking into Darkseid's fortress while Wonder Woman defends him from attacking parademons. Just as she's about to be overwhelmed, the rest of the League shows up and cleans house.
Dragon Age: Origins. City Elf origin has one where the hero is too late to the rescue. However the victim still describes the Warden-to-be like this afterwards if you still took revenge.
Subverted in Dragon Age II where you go to rescue your mother from the hands of a deranged serial killer. You beat the boss and good new everyone, she's not dead! She gets up, you breathe a sigh of relief and everything is perfect... or not. You're too late, and all you can do is watch her die slowly and in great pain.
Happens in The Lord of the Rings Online in a quest where you go into the Barrow-Downs, not long after Frodo and the hobbits passed through there. At the end of a dungeon, you run inte a powerful wight that you can't beat, because he restores his health to full everytime it gets too low. Enter Tom Bombadil, who collapses the roof on top of him, allowing you to escape. You can later return to that dungeon to destroy the wight for good.
Prince of Persia: The Two Thrones has a rare inversion - "All hail the Prince of Persia! A greater hero the land has never known! You have saved the people of this city, and we have come to repay the favor!" It's not often the crowd comes to rescue the hero.
In Tales of the Abyss, Guy turns a hostage situation around by skydiving off the Tartarus, using the gun-wielding Legretta to break his fall, and rescuing the hostage in a matter of seconds. As if that were not impressive enough, Legretta immediately attempts to shoot Guy while his back is turned, only to have the latter casually block the bullet with his sword.
Enter the amazing Guy!
The arrival of the line piece in Tetris is usually this.
In Starcraft II, Jim Raynor pulls an epic one by saving General Warfield and wiping a Zerg attack wave on Char. When thanked by Warfield, with a gunship silhouetting him from behind and sniper rifle of doom in hand, Raynor replies "All in a day's work General!"
In Heart Of The Swarm, Kerrigan finally reaches Arcturus Mengsk, only to be incapacitated and tortured by a Xel'Naga artifact that kills any Zerg in the vicinity. Mengsk starts to gloat, forgetting that the device doesn’t affect Terrans...
Jim Raynor: Change of plans, Arcturus.
In Mega Man Legends when you release Mega Man Juno he is about to initiate the carbon reinitialization program and kill everyone on the island you crash landed on. In order to make sure Mega Man Volnutt/Trigger doesn't interfere he traps him in an electrical field. He would've been stuck there if Tron and Tiesal Bonne hadn't showed up.
Their conversation just as they ran to turn the thing off
Tiesal:Oh, here's the problem. Hey Tron! How do you stop this thing?
Tron: Oh this? LIKE THIS! *kicks it turning it off*
In Assassin's Creed I you get to save citizens from guards harassing them and they return the favour by forming vigilante packs who help Altaďr fight guards or catch fleeing targets. Although this was absent in Assassin's Creed II, it returns in Brotherhood. This time, the citizens become novice Assassins under Ezio.
Plot-wise, there was the time Altaďr was overwhelmed by enemies at Masyaf but they are scattered by a swarm of throwing knifes from Malik and three other assassins. Ezio's first mission with the hidden gun. The thief says to stay back or he'll kill the courtesan because he mistakenly believes that a Master Assassin has to be near you to kill you.
In Star Wars Bounty Hunter, Jango Fett and Zam Wessel meet for the first time and partner up, only to part ways later over a misunderstanding. Near the end of the game, Fett is shackled to a table and being tortured by the Dark Jedi Big Bad, only for Zam to arrive in an attempt to kill her. Her shot is deflected back into her, but before Zam can be finished off she fires a shot into one of Fett's cuffs, allowing him to drive off the villain and save both their lives.
At the end of the first level in Singularity, the Big Bad has the player at gunpoint, just killed his partner, and things are looking grim. Then the British agent Kathryn Only-One-Name sends him and his men ducking under a hail of gunfire and directs the player along the path to safety as soldiers fire at his back. Later in the game, the player repays the favor by kicking open a door and shooting the two soldiers that have Kathryn at gunpoint.
At the end of Dead Space 2, Isaac has won the day yet again, defeated the apparition of Nicole, killed the Marker and excised the tainted sections of his own mind. Badly injured and with the remnants of the Sprawl undergoing a cataclysmic reactor meltdown, he sits down and waits for the end. Then Ellie flies a fucking gunship through the ceiling to haul Isaac's ass out of there.
In the last dungeon of NieR, The Masked People show up just in time to save the heroes from being killed by a giant boar. They also have a Heroic Sacrifice when they hold off the Boar so the party can continue.
Pokémon Diamond and Pearl (and Platinum) Just when it looks like you'll have to deal with Commander Mars and Commander Jupiter at the same time while Cyrus destroys the universe, your rival shows up and helps you defeat them both.
In Platinum specifically, when you confront the enemy team boss, it turns out he was prepared for your interference and counters your strategy for derailing his plans. At that point it seems like you cannot do anything... and out of nowhere Giratina shows up and swallows Cyrus into the Distorted World, at the same time freeing Dialga and Palkia from his control, and stopping all of his plans single-handedly. Unfortunately, this does create another crisis, but this new crisis is one the player is capable of solving.
Pokémon Black 2 and White 2 Just as Ghetsis is about to deliver a chilling thrashing to your character with Kyurem's Glaciate, N swoops in with his Zekrom/Reshiram and uses Fusion Bolt/Flare to destroy the attack. Unfortunately, Ghetsis was not only prepared for this he expected it.
In Pokémon Mystery Dungeon: Gates to Infinity, you, your partner, and Emolga confront a pair of conning Pawniard for the sake of rescuing Dunsparce from them. They respond by calling out their buddies, a pair of Galvantula and Whirlipede. However, this in turn prompts the appearance of Virizion, Gurdurr, and his two Timburr apprentices, which leads to a seven vs. six brawl. Later on, the hero ends up separated from their partner, then cornered by Croagunk, a Gigalith, and a Chandelure. They manage to defeat the three of them, only for reinforcements to arrive in the form of Salamence and a mob of Excadrill. Right as the dragon is about to finish them off, Hydreigon suddenly makes his first appearance in the flesh as an unexpected savior and interrupts him with a Dragon Pulse to the face before flying the hero to safety.
In The Reconstruction, this is subverted. After the world is destroyed in chapter 6 and the Big Bad kills or enslaves everyone, Dehl's guild is the people's only hope...but they aren't able to come until it's far too late.
Near the end of Leisure Suit Larry 5, Larry's home flight starts plummeting from the sky due to the pilot's contract expiring, but being a former flight simulator salesman, he takes control and safely lands the plane.
In Xenoblade after re-locating Metal Face he summons multiple copies of the Mechon you just busted your ass trying to beat, it looks hopeless... until Shulk and co. get bailed out by Dunban and Dickson. The rescue however fails until they're bailed out by another Big Damn Heroes by an unidentified man.
Later in the game, Colony 6 gets swarmed by Telethia threatening to destroy it. Two major NPCs are about to be blasted away...and right on cue, an army of giant Mechon flies in to save the day.
In the fourth chapter of Tales of Monkey Island, LeChuck shows up at the last minute and bails Guybrush out of court. Though this was actually a Villainous Rescue, as LeChuck is only doing this in order to let Guybrush power up La Esponja Grande and get all of the Pox out of everyone in the Gulf of Melange, so that LeChuck can kill him later.
In the fifth chapter, when Van Winslow attacks LeChuck's ship with an army of merfolk and saves Guybrush from being murdered by a demonic Elaine.
Zoey, Francis, and Louis give you covering fire at the main intersection in the finale of The Passing and they will very likely save your ass from the horde and Tanks in the area.
In Heavy Rain, if both Ethan Mars and Norman Jayden at least make it to where Ethan's son is being held, then Jayden gets a BDH against the Origami Killer by tackling him right before the killer can shoot Ethan.
Earthbound gives us this gem in the midst of a boss battle: "All of a sudden, some guys rushed into the room! It was the Runaway Five!"
The Mana Khemia games give you the option to swap an out-of-battle party member in for an active member who is about to be attacked, sometimes with additional effects such as healing or invincibility. Muppy in particular can shelter the rest of the party in his potlike ship when he does this, protecting them from large-scale attacks.
In the first Breath of Fire for Super Nintendo, the kingdom of Winlan, a land inhabited by winged folk, has had their king poisoned. The Princess and two guards attempt to defeat an evil wizard and secure his antidote. However, he releases special gas that severely weakens the winged folk's race only. The Princess and one of her bodyguards get curb stomped in a hopeless boss battle, while the other guard goes back to the castle to convince the Hero to help. It's up to the hero, who isn't affected by the poison, to lay the smack down on the wizard and save the Princess. It's possibly one of the most emotional big damn heroes moments in the entire game.
Subverted in the Consular story of Star Wars: The Old Republic. Senator Grell is kidnapped, Tharan and Holiday do an epic job of calculating the kidnapper's location from minimal data. You and Nadia (the Senator's daughter and, at that point, your unofficial padawan) storm aboard, lightsabers lit and ready to raise hell. Only...it's just barely too late to save the Senator, who has been tortured to death. The kidnapper is a Sith that's been MindRaped so much he can't recall his own name, much less any useful information, and is left a babbling husk on the floor after he's expended his use.
There are some over the course of Hatoful Boyfriend. You-the-heroine can be this for Yuuya when he's caught snooping, or you can just damn him. You-the-heroine can also be this for Anghel. In Bad Boys Love the bleakest point is salvaged by Sakuya and Okosan, who helped Sakuya out of his Heroic BSOD. Holiday Star has a number of such moments, and on two occasions they are nested - Yuuya comes in and turns the tide, but things get too much for him and Doctor Shuu of all people steps in.
Garry does this in Ib under certain circumstances, saving Ib from a psycho knife-wielding Mary.
In any match of Monaco: What's Yours is Mine there is a good chance someone will end up being this for other players or even the rest of the team.
In the last act of Rhythm Thief & the Emperor's Treasure, Phantom R is forced to fight the real Chevalier Diabolique, who are massive robots. Charlie and Inspector Vergier arrive and help him fight them off. Not too long later, Phantom R bursts in and saves Marie from Napoleon, who he proceeds to take down in a sword fight.
In Chapter 5 of Danganronpa, Naegi gets executed. Or not, since Alter Ego turns off the machine just in time to save the day.
In Saints Row: The Third some of the Survival missions involve the Boss showing up to save innocents from the Syndicate.
In Hyrule: Total War Zelda I is about to get killed by Ganon's minions when Impa shows up.
Star Trek Online loves to do this, with their your faction swooping in to save your hind quarters or you saving a few Red Shirts caught in the crossfire. There's even skills and items that allow you to keep doing this!
DC Universe Online has these frequently in the hero story missions, with your Plyer Character being on both sides depending on the mission. The tutorial has Superman be teleported in to help as you're nearing the end, while later missions include rescuing Robin, Supergirl, Flash, Nightwing, and a few others when they're captured or cornered by villains.
The second part of Grisaia No Rakuen is all about the Mihama girls planning a rescue for Yuuji and the third is about actually carrying it off. They need their Own Big Damn Heroes though, which comes in the form of Millie with an attack helicopter.