The ending of Skies of Arcadia, of course. Rather unusual in that Gondor never actually called for aid; rather, everyone just showed up because they knew that the heroes were the only ones crazy enough to go head-to-head with the Big Bad, and wanted to join in on the fun.
In Freelancer, the first half of the game is about finding someone who can identify the artifact that fell into Trent's hand. Near the end of the game, the Order calls the Outcasts and the Blood Dragons to help them against the Nomads.
In the first, it's played straight, on both sides—the nations of Bracada, AvLee, and Erathia coming together to face Nighon and Eeofol (who later drop out of the war). Later, the necromancers of Deyja make an alliance with Erathia to stop the necromancers' own king, who has grown far too powerful for their liking.
In Armageddon's Blade, the witch Adrienne asks Erathia for aid against an invasion of undead that threatens both their borders. Erathia, too caught up in its other problems, declines. Meanwhile, AvLee and Erathia are allied briefly against Eeofol, and then Erathia finds new allies in the Conflux towns, before the queen of Erathia abdicates in order to pursue the war with more vigor, Erathia having grown tired of war. Finally, the last mission of that campaign has to be completed within two months—or Eeofol's call for aid from Nighon will be answered.
In going against Bodhi's guild towards the end of Baldur's Gate II, the player character can form an alliance with a paladin order, the thieves' guild, and the Companions of the Hall (Drizzt Do'Urden and friends) against them. Doing so naturally makes the battle much easier.
In .hack//G.U. Redemption, Haseo and Zelkova use their influence to get help from all the players of "The World" to assist them in stopping Cubia.
The Courier can pull this off at the ending battle of Fallout: New Vegas by doing enough of the right favors to the smaller factions in the Mohave.
Super Robot Wars Alpha 3: In the final battle, the dead come back to support the player. Irui even joins the battle with the same stats as she had in Alpha 2 if you got enough battle masteries
In EarthBound, beating the Big Bad requires the combined prayers of almost every named character in the game, including the player, by which we mean the person holding the controller..
Final Fantasy IV: When the villains summon the giant world-ending monster, just about everyone you've ever helped, including all your ex-party members except the one that really died, shows up in tanks and airships and starts blasting away.
Then, at the end of the game, Everyone prays to give your party the strength to defeat Zeromus. Even Tellah and his daughter Anna show up.
Something similar happens in Final Fantasy IX, where the air forces of the entire world arrives to save the heroes from a hundred dragons emerging out of The Very Definitely Final Dungeon, and Final Fantasy X, the people of Spira sing the Hymn of the Fayth, the only way to calm down Sin, in order for the heroes to stand a chance of fighting it.
In Ōkami, the prayers from all the people of Nippon, inspired by Issun, are what revives Amaterasu and restores her full divine glory. Cue the Theme Music Power-Up and the final boss fight.
Dawn of War mixes it up a bit at the start of the Space Marine campaign, in which you get to beThe Cavalry for a hard-pressed Imperial Guard unit that's desperately trying to Hold the Line on the surface.
The story mode of Mortal Kombat vs. DC Universe features this trope. Regardless of whether the player chooses to play as the MK or DC fighters, the chosen world's heroes end up having to work together with their villains to deal with the opposing faction's fighters, whom they initially see as invaders until Dark Khan finally makes his appearance for the final showdown.
At the end of Warcraft III, the night elves had to ally with the humans and the orcs to defend their World Tree Nordrassil. The first alliance stuck and continued into World of Warcraft, the second didn't.
At the end of Space Channel 5, Ulala fights alongside her rivals Jaguar and Pudding, and every person who she's directly or indirectly helped throughout the game come out to lend their support and dance energy.
The second-to-last mission of Ace Combat 5 starts with squadrons from both the Osean and Yuktobanian armies supporting you in disabling the Belkan super weapon control station after hearing their leaders' speeches.
Mission 12 of Ace Combat 6 requires you to evade no less than 30 enemy fighter jets. After a few minutes of dodging missiles for your dear life, every air squadron in the game comes to your aid (including a squad of electronic support planes).
You spend the main part of the game doing this in Dragon Age: Origins. The bulk of the questline involves solving whatever problems are preventing them from being able to dispense said aid. The Elves, Magi, and Dwarves all greet your Warden with variations on, "We'd love to help you, but..."
In Mass Effect 1, near the end, should Shepard decides to save the Council, cue the Alliance Fleet pouring through the Relay and immediately pull of a Big Damn Heroes moment, in addition to turning the tide of the battle.
Asari: It's the Alliance! Thank the goddess!
Mass Effect 3 is filled with this, as Shepard finally cashes in all the goodwill they've potentially earnt over the course of the previous two games, depending on their actions. If Shepard plays his/her cards right, (s)he can look forward to calling on the aid of the Turians, Krogan, Salarians, Asari, and Quarians, and possibly the Geth and the Rachni.
In the Leviathan DLC, Shepard even gets an Eldritch Abomination on their side, part of The Remnant of the first race harvested by the Reapers and whose form the Reapers modeled themselves after. Yes, that race!
Your quest in Dark Sun: Shattered Lands is to get military aid from neighbouring cities. That's the object of the entire game.
Touhou 11: Subterranean Animism has Reimu and Marisa being helped by various kind of people (who each have their own reasons) on their fight against the subterranean horrors. Yukari is interested in maintaining peace, Aya is going for scoop, and Nitori is defending her rivers — which makes Marisa the aid. In a twist, the unleashing of subterranean horrors themselves is Rin's call for aid. She can't stop her best friend Utsuho who is drunk with (nuclear!) power, so she hopes that someone strong enough from the surface will stop the crazy hell raven.
Touhou 13: Ten Desires: An aid was called for, but it's not for the heroines. The heroines come the source of the problems and solve it anyway before the supposed aid even come.
Pokémon Black and White: Bianca calls for the Unova Gym Leaders to come and fight versus Team Plasma at N's Castle, after the Elite Four challenge.
In Darksiders, this is what happens when War gets Uriel to break the seventh seal, summoning the other three Horsemen.
Uriel: You will be hunted! The White City for certain...the Council...and there will be others! You would wage this war alone?
War: No. Not alone.
To fight against Nero, Blanck, and eventually Tartaros in Solatorobo, Red enlists the help of Opéra and the Kurvasz, who then put out a call for everybody to help. And they do.
Diablo III: An obvious homage, a quest in ACT III has your character being instructed to light five signal fires along Bastion's Keep's walls. Somewhat averted since the King of Westmarch, the leader of the arm you're asking help from, dismisses the request since they did not believe Bastion's Keep was really being attacked by demons.
In the fourth level of Iji, you're tasked with sending a distress signal to the Komato, a race of aliens who are at war with the aliens already invading Earth, in the hopes that they'll take care of the problem for you. This backfires massively.
Depending on your alignment, the final phases of the second Knights of the Old Republic game invokes this. A light-side hero will see the Khoonda Militia, TSF Forces, Onderon Royalists, and Mandalorians rally to their side.
The Jedi Consular's arc of Star Wars: The Old Republic is entirely this, from Act 2 onward. There's an alliance of powerful, but politically neutral worlds that don't much like the Republic, but like the Imperials even less. The Consular gets tasked by the Supreme Chancellor of the Republic to essentially go door to door and enlist their help. By the time you roll into Imperial-occupied Corellia, you have the largest droid and weapon factories in the Core from Balmorra (and their most notorious "Freedom Fighter" as a party member), medical supplies from Manaan (with oceans producing a near-miraculous healing substance), a Voss Mystic (who normally are forbidden to leave the planet due to their value) and his entourage of healers and commandos, the Shakari army looking to avenge an attack on their monarchs and the murder of their Senator (and under the command of the Consular's padawan), and an army of Esh-Ka (a species not even the Rakata wanted to cross swords with when they conquered most of the galaxy)