Heads I Win, Tails You Lose (Grahf Rule): It doesn't matter that you won the fight with the boss monster; the evil task he was trying to carry out will still get accomplished somehow. Really, you might as well not have bothered.
Call of Duty: Modern Warfarehas this in part one and two. In part one after rescuing a downed helicopter pilot, the entire city you're in is struck by a nuclear blast, killing both you and presumably the pilot you rescued. In part two it happens multiple times.
The third Modern Warfarezig-zags this trope when playing as the FSO agent. At the end of the level, you find the Russian President and get to an evac chopper - only to immediately get shot by Makarov and lose the President. That said, in Spec Ops, there's a mission that starts immediately after this - where you get up, attach a surpressor to your pistol, and go save the President's daughter, Alena. That said, the next time you hear from Alena is when she's frantically calling for help because everyone in her security detail (including the FSO agent that saved her) is dead.
In James Bond 007 (Game Boy), after you defeat the final boss General Golgov and the remainders of his mecha disappear from the screen, you can still read his next lines, stating that although you have defeated him, you cannot escape the destiny he has created. Next you free Zhong Mae and she tells you about disarming Golgov's nuclear missiles. Quite a sense of urgency and I've-got-to-save-the-world - although this is not a timed mission.
Metal Gear Solid, you beat Sniper Wolf after much backtracking to one of the earliest areas in the game, the 2nd floor basement of the tank hangar. Immediately afterwards you are captured and hauled back to the first floor basement of the hangar, one floor above, for a torture session.
And in the first sequel, it doesn't matter how quickly Raiden shoots Vamp during the sniper section. Emma still gets fatally stabbed by him after the fight ends, even though if she dies during the actual boss fight it's game over.
The first game of the series has the battle against Leon in Traverse Town. If you win, you still receive that "Exhausted Sora" cutscene, but if you lose, well, then you just simply lose in the cutscene as well. Lose/lose situation, in other words. You get an extra reward later if you beat Leon, so it isn't that bad.
The same applies for Cloud later in the Olympus Colosseum.
Batman Arkham Asylum has Batman trying to save Dr. Young from Zsasz. You have to take Zsasz down stealthily; if you wait too long or rush into the room, he will slit her throat. Immediately after you rescue her, Dr. Young gets killed in the following cutscene. Well damn.
Oh, its much worse than that - With the exceptions of Commisioner Gordon, Aaron Cash and various guards scattered throughout the game and Warden Quincy Sharp, every hostage in the game you rescue will die later offscreen. You rescue them, tell them to stay put and hide somewhere, and when you pass through that location agiain you can find their corpses, killed by the Joker's crew, even they did exactly what Batman told them to and hid. To twist the knife further, the aforementioned Warden Sharp turns out to be an Ax CrazyKnight Templar who has been having patients tortured and murdered; when you go back to where you left him, he has simply vanished, and in the sequel is actually the Mayor after taking the credit for Batman saving the day (though this Karma Houdini turn is mitigated somewhat when the sequel shows he was also Brainwashed and Crazy).
The second game has fight against Atris, though in here, win or lose doesn't matter, she will beat Handmaiden anyway.
Knights Of The Old Republic II also has the Exile's first fight against Darth Sion on Korriban. If you are killed, you're dead, but after Darth Sion heals himself a few times Kreia tells you to run, and run you do. This is extremely frustrating since you can do the planets in any order, therefore it's entirely probable that by then you're rather powerful and Darth Sion can't hit you, let alone do enough damage that you can't simply heal yourself easily with the Force.
The Sith Inquisitor storyline in Star Wars The Old Republic contains a rather egregious example: during your battle against Darth Zash, you must win to get defeated in a subsequent cutscene (and barely saved by your faithful companion); if you are "killed", you can just call a medprobe and get revived right there, restore your health and attack again. The Fridge Logic of the situation is that Darth Zash wanted you knocked out (not dead!) all along, so she could take over your body—but the MMORPG mechanics force her to chivalrously wait for you to get up and beat her fair and square before she can unleash her powers and knock you out in a cutscene.
Persona 3 has this as, of all things, the expected Final Boss battle. (The true Final Boss battle, however, is thankfully a scripted Foregone Victory instead.) Somewhat justified in that they've been hammering into your head that you cannot win against this, the only thing you're doing is dying with dignity.
Persona 4 gives us Shadow Rise. If you die against her, it's a Game Over, if you lower her health enough she will perform an Enemy Scan on your party and you will no longer be able to hit her at all. And it is still Game Over if she kills you after this happens, you must hold off against her until the cutscene three rounds later.
Rogue Galaxy has the masked guy. You fight him quite a few times, and in every single fight but the last, after a certain time elapses, you're treated to a cutscene with your characters saying "This guy's too strong!" and "We can't beat him!". This is especially annoying since he's not really that tough—you can end the fight early by dropping his HP to a certain amount, and if you figure out the right strategy, you can get him to that amount in under a minute.
Happens annoyingly often in Klonoa Heroes: Legendary Star Medal. You fight through a swarm of giant mooks, you get overwhelmed by a bigger swarm. You beat Boxmaren, it regenerates and multiplies endlessly until Pango shows up and destroys the computer controlling it. Defeat Joka, he goes One-Winged Angel and whomps you so badly you don't even get a cutscene of him actually doing it, just a bit of dialogue stating you lost.
Final Fantasy VIII pulls this one several times. The first occurs inside the first sequence involving Lunatic Pandora, where after fighting waves of enemy Mooks, the last one brings two party members down to 1HP immediately if they are not already KO'd to facilitate a plot point. Another occurs when you fight against Edea in Disc 1, which, depending on how much magic you've stocked up, is either a fair challenge to stay alive or a pushover. However, the fight against Edea ends with her using what later turns out to be her Limit Break, so it actually makes sense that she could oneshot Squall with it.
Final Fantasy IX pulls a non-cutscene variant several times: all the battles against Beatrix (early in the game) and Kuja (later on) play out as normal boss fights until you defeat them, at which point they automatically pull out an attack which reduces your entire party to 1 HP apiece, forcing them to surrender so that the plot can continue.
Kuja's case is actually him using an attack that just automatically kills the entire party.
Vergil in Devil May Cry 3 after the first boss fight with him. Doesn't matter if you were hardcore enough to No Damage Run over him - he still stomps on Dante afterward. It's not quite as annoying as it might be, though, because you saw part of the fight in the opening cutscene and thus see it coming. Dante is like this in Devil May Cry 4 for the last battle against him.
The story-important Arena battles in .hack//G.U. are played exactly like this for no other reason than Haseo needs to be backed into a corner to unleash his Superpowered Evil Side.
The first fight with Alkaid has her team automatically activate their Beast Awakening when Alkaid herself is dropped to 50%. To say nothing of the fights where you're winning so easily you may as well be smacking around unarmed small children with the flat side of your BFS, only to have a cutscene activate with Haseo on his knees, panting from the exertion.
In Eternal Sonata, the characters, having just beaten the massively-large Tuba who started a fight with them "for fun", allow themselves to be arrested by the guards.
Then, after you beat Tuba a second time, he knocks the entire party off a bridge.
This happened WAY too many times to be acceptable in Dragon Ball Z Budokai Tenkaichi 2. You could be pingponging the bad guy around the map, blasting him with the strongest attacks in your arsenal and have all your health remaining... and yet the cutscene showed your character in their "weary" pose, having supposedly been badly beaten. Yes, SUPPOSEDLY. There's not even a cutscene where the bad guys suddenly pound them, the goodies win... and then are shown all tired out, complaining that the enemy is "Too strong", while the bad guy is standing with nary a scratch. This got REALLY FREAKING RIDICULOUS after a while. Many people were NOT amused with this.
Averted in BT3. When a battle called for the bad guy to win, this time around you played as the bad guy instead. And when there were fights that could lead to this, beating the bad guy shows your triumphant good guy celebrating their victory. Sure the next episode didn't change, but it was much more nice.
Back in Ultimate Tenkaichi's "Hero Mode" (Basically a Create-A-Player Gaiden Game): After defeating Omega Shenron, no matter how badly you beat him and no matter how high your stats are, he'll strip you of the Dragonballs you've gathered, re-scatter them, then vanish, forcing you re-find the Dragonballs and re-fight most of the missions. Witness Lanipator's Angrish filled reaction to this here.
Guild Wars Factions has the Big Bad kill the party in a cutscene after the Vizunah square mission. Fortunately, everyone got better, thanks to some envoys.
Similarly used in the Naruto: Clash of Ninja games' story mode. Even in fights where the "heroic" character gets soundly thrashed, you still have to win... and are rewarded with a cutscene where you get stomped.
Inverted in Jade Empire, when you use Sun Kim to fight Death's Hand, win or lose does not matter, since Death's Hand will lose anyway. If you do win, though, you can gain some extra reward or bind Death's Hand as your follower.
Dispute this, too. Sun Kim wanted to finally die. The only way this trope happens is if you bind Sun Kim.
There are several bouts in the WWE Day of Reckoning games where, when you're just about to win (i.e. the ref's hand is about to hit the three, or your opponent is just about to tap out), you are suddenly jumped from behind by another wrestler.
WWE games have this a lot, the storylines are seemingly not at all dependent on what you do in the ring.
Somewhat acceptable, as the storylines are scripted in the actual WWE as well. And interference by a third wrestler is commonplace.
Not quite as acceptable in some of the WWE titles, though, where these scripted losses actually will negatively affect your records and stats.
Mega Man Maverick Hunter X features this as the Final Boss battle if you play as Vile. Beat X and Zero, and the following cutscene shows them seriously damaged. Then they pull themselves together, stomp you with one shot, and leave you to die. Great reward.
When you play as X, the intro-stage battle with Vile has been changed from a Hopeless Boss Fight to one of these. You have to do a certain amount of damage, but then Vile will simply waste you; Zero's entrance then proceeds on schedule.
In X5, no matter how badly the player wastes Zero (as X) or X (as Zero), Zero's Sōgenmu or X's Soul Body attack from the previous game will be pulled out of nowhere to turn the fight into a draw.
Aladdin (Capcom) has this for the final boss (Jafar in Scaled Up form): after you see a cool death animation for him, he comes back and kicks Aladdin's ass. You still won, but if it weren't for this, the ending of the game and the ending of the movie wouldn't be the same. (Aladdin (Virgin Games) finished after killing Cobra Jafar, possibly to avoid this kind of thing.)
Severely overused in Baten Kaitos Origins. This happens so often that it actually drives the main character into a Heroic BSOD over his constant losses when anything other than his own life is actually at stake. The fights usually end with an unavoidable attack from the boss, then a villain coming out of nowhere to blast the boss into pieces and gloat at you. (Especially egregious in the Lava Caves; how the hell did Valara get that mecha in there without anyone noticing?!) Just to make it more infuriating, some of those bosses are tough.
It's done in the first game as well, although not quite as much. It still gets irritating when you're beating a boss into the ground, and then the next minute your characters are flipping out about 'how tough this thing is'.
Mega Man Battle Network does this a lot. Almost every time you beat a WWW or Nebula boss, he'll pull himself together and escape with whatever Plot Coupon you were trying to keep out of his hands. Sometimes the boss even has a doomsday attack in reserve — cue Chaud and ProtoMan to save you from it, then insult you for being unprepared.
In Castlevania Curse Of Darkness, the first fight with Trevor Belmont is like this. It's a little less irritating than usual, since you don't actually have to beat Trevor to get the "you still lose" cutscene, just whittle away a small fraction of his health bar.
In The Incredibles video game you must defeat the second OmniDroid (which Mr. Incredible never really managed to fight in the film), but immediately afterwards you are treated by a clip from the film showing Syndrome arriving and chasing Incredible down a waterfall.
Done very subtly in Paper Mario The Thousand Year Door. When the boss Doopliss copies Mario, he also switches places with him and reverts the real Mario to a shadow. You must defeat the shadowy Mario in order to continue the game, which might make sense at the time, but not so much in retrospect.
Also, Zack's final battle. Which is the reason to why many don't want to finish the game.
In the last mission of the Hierarchy campaign of Universe At War your mission is to defeat a single boss unit. No matter what force you have at the end of the battle the cutscene shows your army defeated by the enemy forces and the boss killing you.
Same with the Novus campaign; you're tasked to defend a portal that overloads and explodes in the end when you win.
The battle against KagekiyoTaira in Genji in the first chapter. You can get your revenge in the second chapter after your training in the Golden Temple.
At least two skill checks in the Billy Vs SNAKEMAN storyline quests are not to succeed in what your character is attempting, but just to lose "in an awesome and non-fatal way".
Same goes for the video game version of Harry Potter and the Order of the Phoenix with the battle between Harry/Sirius and Lucius/Bellatrix. I know the plot demands it but it is still rather frustrating.
After you defeat Rictus in Anachronox, he will suddenly recover for no reason and curbstomp the party in a cutscene. Justified, however, since Rictus is a literal comic book villain and pulling cheap moves is par for his course. Boots will even lampshade it, moments before it happens, by recalling a similar fight for the comics.
Happens with all five of the final bosses in Odin Sphere if you don't defeat them with the character that is mentioned in the prophecies.
Although Ingway's transformation into the Beast of Darkova can be broken by anyone who fights him, only Cornelius survives the experience.
If you defeat King Gallon with anybody besides Oswald, he immediately recovers from his wounds. Only Oswald can defeat him because in addition to being of Titanian royal blood (necessary in order to defeat the Beast of Darkova), his power comes from the Queen of the Dead who cursed Gallon into his undead form.
If you defeat Onyx with anybody besides Mercedes, he will be completely unharmed after the fight is over. The game doesn't exactly explain why only Mercedes can kill him, but the prophecy says that he will be stopped by the World Tree. Like all fairies, Mercedes has a True Name derived from Norse mythology - in her case, it's Yggdrasil, and a huge tree grows in the spot where she dies.
Velvet is the only one who knows enough about how the Cauldron works to disable it without destroying it, making it possible to use it to break down the Psyphers and release their absorbed life energy back into the world to prevent its death. Anyone else cracks the Cauldron's core and dies in the massive explosion that results.]]
If you defeat Leventhan with anybody besides Gwendolyn, they're killed in the subsequent fall from the sky. As shown in the good ending, Gwendolyn is caught by Oswald, provided he also survived his own battle.
Baroque's plot is practically built on this. Dying is a key way to advance the plot. Not to mention, once you actually win, It has the same effects as dying. Whee!
While it doesn't come with a curb stomp after the fight, winning against Mukai in The King of Fighters 2003 results in him standing up, back in his standard battle pose, with your characters remarking (more or less) how you barely scratched him (and sometimes how he even seems unfazed). He leaves afterward, with only a hint of the trouble that's to come.
The Human mission 9 involves defeating Protoss outpost, without harming the Zerg base. After eliminating the threat, the Zerg overrun your base, facilitating Kerrigan's Face Heel Turn.
Theoretically. Rather foolishly, they didn't make that powerful a force. As such, it's quite easy to destroy it with a few well placed bunkers, battleships, and siege tank emplacements, that you spend much time building to chase down the old enemy. Doesn't change the cutscenes, though.
This mission is a prime example of Gameplay and Story Segregation. Whether or not you constructed a large enough force to take out both the Protoss and the Zerg bases is moot considering you more than likely built a couple of transports to complete the mission and there should be nothing stopping you from loading Kerrigan onto one and flying back to the fleet in orbit around the planet.
In Protoss mission 7, You have to protect Tassadar from the Conclave. Once you destroy part of it Tassadar surrenders. But you win and can rescue him in next mission.
In the Terran Campaign of Starcraft 2 you have to make a hopeless Last Stand against endless hordes of enemies in the vision of Bad Future. Eventually all your forces will be eliminated, but you are still obliged to kill a certain number of enemies to... make the ancestors proud, I guess.
In the Wrath of the Lich King expansion of World Of Warcraft, the eponymous Lich King is actually Dangerously Genre Savvy, but due to Obfuscating Stupidity comes off looking like a Bond Villain for most of the game, even in the final battle. Then, at 10% health, he reveals his Xanatos Gambit by suddenly killing the entire party and proceeds to raise them as his new generals. Had it not been for Tirion Fordring shattering Frostmourne, the Lich King would have succeeded.
Used aggravatingly often in the Cataclysm expansion. Many is the quest where the second you complete the required objectives, you get captured or cornered by mobs who, by all rights, shouldn't even stand a chance against you, and you can do nothing about it. This is most blatant by far in Vashj'ir and Uldum. Vashj'ir is at least convincing about it (through the entire zone's quest line, you're heavily outnumbered by the Naga and are on the run), but Uldum's instances of these are just pure Cutscene Incompetence.
In the first of the RedAlert series one Soviet mission was to capture a Chronosphere. If you approach it before destroying radars (as warned), it explodes and you lose. If after, it still explodes, but you win the mission. The generals in the briefing room shift blame from you to the intelligence, and your last chance for victory is a full assault on London.
The online Flash game Red Moon has a particularly Egregious example of this: after spending the game watching the heroine get bossed around and outright abused by her walking tutorial boyfriend, you reach the Emperor and beat him... only to see a cutscene where not only does the Emperor win easily, but he defeats your character first, leaving the NPC to do most of the fighting before running away. Then, to add insult to injury, she aplogises to him for not being strong enough. And did I mention that's the end of the game? What the hell!?
The creator of that game loves this trope. Red Moon is a prequel to the Armed With Wings series, and in Armed With Wings 2, you play as the villain. At the end of the game, you face The Hero. Die against him, you lose, beat him, and a cutscene follows where he pulls a One-Winged Angel, reveals he is the avatar of God himself, resurrects all the people you've killed over the course of the story and seals your Villain Protagonist in a white room for all eternity. Justified, however, because this Villain Protagonist is vital to the plot of the next game and as such must be sealed, not killed.
The following game, Armed With Wings 3, also has one of those as the first boss which you defeat (pretty easily, as he's the first boss), only to have him get up and jump your protagonist, who is taken by surprize from behind and totally defenseless, saved only by his mother. Same game has a Hopeless Boss Fight, too.
Not necessarily a hopeless boss fight, but if it becomes apparent that the player is actually capable of winning despite being overpowered, then the game just jumps to the cutscene.
In a series notorious for it, the concept is completely turned around in Culmination, an interquel taking place during the lategame story of Armed with Wings 3, a Foregone Conclusion setting explaining how and when the old hero died. You play him for most of the game and then you face off against the Final Boss...only to realize that you're controlling HIM in this battle now! Cue the player using the Emperor's Purposefully Overpowered arsenal to utterly destroy his earlier player character.
The Force Unleashed has this in the Light Side ending of the final boss battle. Once you've defeated the Emperor, the final cutscene shows that Starkiller is killed anyway while distracting the completely unharmed Emperor from some escaping senators.
The Dark Side ending plays with this a little. For the final boss, you kill Vader but then in the cutscene afterwards, Starkiller turns on the Emperor, who (probably) effortlessly defeats him. You don't die in this ending but you just become a replacement for Vader. It still counts though.
The squeal also has this in the Dark Side ending. You defeat Vader and prepare to kill him when suddenly, a perfect clone of Starkiller comes out of nowhere and kills not only you but Kota and everyone else who's a threat to Vader.
Of course since Starkiller is Doomed by Canon the first example, which is canon was obviously going to happen anyways. The other two examples aren't canon.
MegaMan Star Force 3 has a mini-game style battle where Geo and Omega-Xis have to fight off a wave of Omega-Xis copies and keep them from invading WAZA headquarters. In the first wave, if you lose, it's game over of course, but if you win, the copies proceed to break in effortlessly via cut scene.
Made all the more egregious in that you're explicitly stated to be stalling for time so Dr. Goodall can get the anti-clone gun working. She gets it working, wiping them all out, which immediately depletes the battery to zip. Then Queentia/Queen Tia summons even more of them, leading to them breaking in.
In many Super Robot Wars games, there would be moments where you take on boss units who in-game can be fairly easy or somewhat difficult to deal with depending on the unit. Then once the units are defeated, mostly to coincide with the units' respective storyline, they would immediately target one of the protagonists with it's strongest attack (usually it's respective series arch rival), completely obliterating it even if you have full health and special skills up.
Sonic Riders, of all games, does this with a particularly irritating race in Story.
The boss at the end of the tutorial in Demon's Souls is nearly impossible to beat — its attacks are fairly easy to dodge, but if you get hit once you die immediately, and given the amount of damage it can soak, you're pretty likely to mess up... but if you do manage to beat it, you end up being killed by another monster in a cutscene, because the plot requires you to die at this point for it to continue. If you do manage this impressive feat, you may obtain his Gray Demon's Soul well before you normally would, so it's not all bad.
X-Men: Next Dimension: Doesn't matter how many robots Forge manages to take out when you control him, he's eventually going to get himself tied up and captured.
An inverted variation happens in Ultima VII Part II: Serpent Isle. After one of your friends is put on trial in Fawn for blasphemy, you're supposed to sneak into the temple, locate the controls for the oracle, and set her to say the truth (as opposed to being forced by the priestess to condemn the accused). If you don't bother to do so, the next day the oracle will, as expected, condemn your friend... and then the resistance (who gave you the key to the temple earlier) bursts in, reveals the whole plot, and arranges for your friend to be freed. Either way, you can't fail this. (A rare case of averting Holding Out for a Hero, too.)
Toy Story has a Boss Battle against the Claw where you, as Woody, have to toss LGMs up at the Claw to knock Buzz down until Sid runs out of quarters. Of course, since the movie has Sid capture Buzz and Woody anyway, the cutscene following this fight naturally has that happen.
On a few storylines, they will justify it with the explanation that beating a boss in game is the equivalent to the character holding their own in the fight long enough for some event (e.g. backup arriving that will scare off the boss) instead of being quickly killed if you lose. Only a few, though.
Happens all the time Suikoden III. Most of the plot boss battles (as opposed to the optional treasure bosses) are this. It...gets a bit tiresome.
Naruto Shippuden: Ultimate Ninja Storm 2 has a nifty variation that's a combination of this trope and Hopeless Boss Fight. It's the fight between Jiraya and Pain. You have to legitimately win the match, and drain Pain's health meter to zero, then in the middle of the fight, Jiraya gets nailed by a sneak attack by one of the heretofore unseen Pain paths, which then leads to an heavily injured, barely playable Jiraya trying to stave off all six Pains. You will lose, but then in the ensuing quick time event, you have Jiraya get back up, and through sheer will, blow one of the Pains completely away with a move that launches his own dying body into the ocean. Heads I Win Tails you Lose has rarely been this cool.
In the Rise of A Ninja and The Broken Bond games the player is also forced to follow the storyline of the anime regardless of their actual performance in the game which leads to losses you can't avoid. It can be annoying to get trash-talked by your opponent in an animated cutscene after stomping them into the ground (Kiba for this editor) and this can cause some plot holes like Sasuke's fight with the Sound Four as they try to tempt him with power by calling him weak... even if you don't resort to using the Cursed Seal (Rage Mode) to beat them. To be fair there is no way Naruto or the other Konoha genin could win against opponents like Itachi or Orochimaru in Part 1 and in some fights in The Broken Bond your real objective is not to win but to survive or use a specific move to beat your opponent.
An example from a miniboss, is Void, from Grand Chase. Basically, you have to avoid his projectiles, which deal decent damage, and more quickly, while dealing a massive 1 damage per hit. After a certain number of hits, he'll warp to the other side of the rather large arena, and start again. After enough hits have been done, a cutscene will happen, where he just steals what he's after, and warps off. If he takes out all your lives, you fail the dungeon. Not so hard in a party, but with slower characters in a solo run, you'll be hard pressed to not lose at least one life.
Possibly in Cave Story after the Core. The Doctor and Misery arrive, teleport the dying Core out, and leave player and Curly Brace behind. Then, the room floods and player seemingly drowns, until Curly sacrifices herself to save him. (unless, of course, you have a certain item)
In the final battle of Ring Of Red, one of your goals is to keep the Prototype mechs used by Weizegger and Ryoko from falling into the hands of the Soviet commander pursuing you. At the end of the mission, Weizegger and Ryoko bothstay behind to hold off the Soviet forces in order to let their teammates escape.
In Ace Combat Zero, Mission 12, you have to shoot down a squadron of Belkan BM-335 bombers supposedly carrying nuclear payloads. If one gets away, it's mission failure. If you shoot them all down, you are exposed to a plot-central nuclear explosion that you just tried to prevent.
In Air Force Delta Strike, Ruth Valentine takes on a solo mission (without orders) to save a stranded hospital ship. No matter how many enemy aircraft you shoot down or the health of the ship, at the end of the Mission Timer, the ship is destroyed by enemy missiles and you suffer a mission failure.
In The Witcher 2 Assassins Of Kings, the first battle with Letho, the eponymous Kingslayer ends with him and Geralt getting into a Beam-O-War which Letho wins and knocks Geralt off his feet. Letho however chooses to spare his life since Geralt saved his a long time ago.
In Destrega, if you play on story mode, this happens a number of times when your character is supposed to lose. If you just suck and lose early, you have to do the battle again; if you get your opponent's health low enough, you'll lose control of you character, who will run around like a schmuck until he or she is defeated.
Several times in the Sengoku Basara series. For a concrete example, look no further than fighting Mitsunari in Oichi's blue path in Samurai Heroes. Once you defeat him, he effortlessly defeats you in the ensuing cutscene.
Luminous Arc 2 does this over and over and over, since it likes to use its boss enemies on several maps in a row. It's even a plot point with Bharva, who can only be permanently defeated on his own home plane of existence.
Notably averted in Deus Ex. After you defect from your corrupt organization, you run away from them for some, but in the end run into a Hopeless Boss Fight and have to surrender. If, at any moment during that time you're "killed", you're instead captured and transferred to the next level anyway.
Many, many missions in FreeSpace 2 require you to not only survive, but to keep some other vessel intact—until it gets blown up by overwhelming force at a particular point in the plot. Sometimes ships even mysteriously explode even if you've killed (or cheated away) every credible threat to those ships; other times the plot will simply hang if the ship in question fails to die. It can get a bit frustrating.
The downloadable Resident Evil 5 bonus chapter, Lost In Nightmares, is essentially a playable version of a flashback cutscene from the main storyline, so naturally its outcome is a Foregone Conclusion, including the playable boss fight against the Big Bad. The bare minimum you need to do to "win" is to simply survive for a certain length of time, although you can also "beat" him in the fight and finish the battle earlier. Of course, winning in this case just means you successfully trigger the canonical Curbstomp Battle cutscene, and you get to watch you and your partner get smacked around for a while.
The first fight against Kai Leng in Mass Effect 3. Lose and its game over. Win and he has a gunship destroy the temple you're fighting in, steals the data both of you are after and escapes while you're busy trying to avoid falling to your death.
The DS remake of Chrono Trigger does this with the Dream devourer, lose and it's game over, win and the dream devourer just knocks you out anyway and you only survive because Schala manages to regain control temporarily and warps you out.
There are a few boss battles like this in Duel Savior Destiny. For example, if you loser while using Lily Sheerfield against Downy Reed in the final route, you get a game over. If you win, your character still gets booted off into an alternate dimension until the endgame and the baddie walks back into the throne room to be a boss fight again, except this time you have to win with an even weaker character. He's still not dead after that either.
A Timed Mission in Drakengard involves you running through a fortress full of enemy soldiers attempting to rescue the Distressed Damsel before the Big Bad kills her. Let the timer expire and you get a Non Standard Game Over. Succeed and you'll find her dead anyway.
In Mortal Kombat 9 during the arc that covers the events from part 3. Sindel is revived and empowered by Shao Kahn and sent to kill the heroes. She pretty much massacres them until Nightwolf is the only one left to take her own. Losing means having to redo the fight, win it, even if you've kick her ass to kingdom come and back again...and Sindel still proves too powerful forcing Nightwolf to preform a Heroic Sacrifice just to kill her.
Non-Video Game Examples:
The Scooby-Doo episode "Which Witch Is Which?" has this exact quote said by Shaggy to decide who enters a scary place. It comes up tails, bringing Scooby to tears.
In Ranma ½, Tatewaki Kuno applies this trope to himself regularly as part of his never-ending quest for a date from Akane Tendo and/or RanmaSaotome. He routinely attacks either girl, proclaiming that if he defeats them then they must allow him to go on a date with them, but whenever they fight back, he also states that if they defeat him, then he will allow them to go on a date with him. That they do not want a date with him is something his absurdly inflated ego prevents him from realising.
In Friends, TOW Rachel's Going Away Party, this is used pretty much to the letter in a coin toss between Rachel and Joey.
This is inverted in an episode of the The Super Mario Bros. Super Show - Toad is cornered by Snifits while trying to climb a wall into Bowser's fortress, so he pulls out a coin and says, "Heads I keep climbing, Tails you let me go!" He then throws the coin in the air, and while the Snifits are looking at it he jumps to a cannon and says, "Guess what? You lose!" before firing and scattering the Snifits.
In the Community episode Remedial Chaos Theory Jeff does a variation of this. In order to determine who has to go get the pizza, he rolls a six sided die with the person to his right having to go if a 1 is rolled and then going around the table for the rest of the numbers. Since there are actually seven people at the table Jeff always wins no matter what number is rolled.
Real LifeTrope Namer. It's a common tactic used by adults on children or older siblings against younger siblings, concerning actual coin flips. The point is to trick the younger individual into not paying attention to the fact that they can't win. It's a surprisingly effective tactic.
Beetle Bailey: Beetle does his best to invoke this when he loses to Sarge in the last game of a ping-pong tournament. The loser has to inform the press, so he does — resulting in a news story about how Beetle lost, with his picture on the page and only his name mentioned in the headline.