In Baka To Test To Shoukanjuu, during the summoner test wars, taking out the class rep is an Instant-Win Condition. Naturally the students usually try to protect their leader, but sometimes the opposing class will bait them somehow and lure them away so as to weaken the rep's defenses and take them out.
This could be said of Zero in Code Geass. During the invasion of Tokyo during the Black Rebellion, Zero's vaguely-justified retreat in the middle of the battle proved to be fatal for his troops' morale, and without him there to lead them they quickly fell to Brittanian forces.
Lampshaded by Diethard earlier in the series, when Zero has gone missing and some of the Black Knights wish to retreat and leave him for dead, rather than risk themselves by sticking around looking for himnote Not cowardice so much as the leaders not wanting to risk everything on the retrieval of one man. Diethard points out that Zero is the glue holding the organization together: lose him and they've lost everything.
Naruto: the army of ninja resurrected by Kabuto was controlled and created by his technique, and thus can be stopped by defeating him. However, just killing him won't get rid of it; he has to actually be forced to stop it.
The first Naruto Shippuden movie features a nigh-invulnerable terracotta army that is animated by an Eldritch Abomination type being called Mouryu. The only practical way to stop it is by sealing this creature, which is in itself a pretty tall order once its soul and body have reunited. Which, in a surprising moment of Genre Savvy, is why they sealed the soul & body in two different places. Mouryu, unfortunately, has shades of As Long as There Is Evil going on.
Space Cruiser Yamato 2. Desslok's flagship has a brigade of robots which Kodai (Wildstar) defeats by blowing up their central computer.
Film
The Avengers. Destroying the mothership causes all the aliens to drop dead. In the DVD Commentary, Joss Whedon admits that he hated having to resort to this trope, but it was necessary to give the heroes a clear victory instead of battling for seventeen more hours of cleanup.
Played with in Battle Los Angeles. The alien invaders are ferocious opponents on the ground and are driving back the US military from Los Angeles and other coastal battlefields even before their drone support shows up overhead. The drones themselves are controlled from a large command center that, when taken out, causes the drones to crash and the United States military to regain air superiority over Los Angeles, but the war is far from over and the aliens remain a tenacious force on the ground.
In Independence Day, the alien ships indestructible force fields and fighter spacecraft are apparently powered by the mother ship. When a virus disables its shields, all of the fighters lose theirs. And when the mother ships are destroyed, the fighters apparently crash (since we never see any of the fighters after the motherships are destroyed).
The rogue robots in I, Robot. Since VIKI was remotely distorting their programming to make them hostile to humans, they immediately became docile upon her defeat.
In the Name of the King: A Dungeon Siege Tale has the Krug, formerly mindless beasts who have been magically uplifted by Gallian to serve as his army. Still mostly beasts, they fight using We Have Reserves tactics. As soon as Farmer slits Gallian's throat, the Krug stop and, after standing around in confusion, drop their weapons and wander off.
Arguably in The Last Starfighter, the Xodan Command Ship's communications turret. It is what allows the entire armada of space fighters to coordinate. Without it, they're not as effective and taken out quickly with a Macross Missile Massacre thanks to the Death Blossom.
Although at least as far as Sauron is concerned, the One Ring was actually his keystone and the reason he still exists in Middle-Earth. The entire country falling into the sea is somewhere trickier to explain...
IIRC, when the One Ring was tossed into Mt Doom, it erupted. That could quite easily explain Morder falling into the sea, depending on the scale of the eruption.
In The Mummy Returns, the unending army of Anubis turns to dust when the title's Scorpion King is killed and ordered to take his army with him. Justified, because whoever kills the SK, becomes the legitimate master of the army. The good army is just preventing the anubites from getting out into the world, they knew they couldn't win on their own.
Oblivion 2013 : After the Tet gets blown up, the drones immediately deactivate.
The curse in Pirates of the Caribbean which rendered the crew of the Black Pearl immortal and unstoppable. Jack and Will break the curse while the crew is in the middle of a climactic battle with Norrington's men, and the second that the pirates realize that their key advantage is lost, they surrender.
The Borg Queen and her Borg in Star Trek First Contact (at least, those Borg who survived the engine coolant spill)
And done in "The Best of Both Worlds" when the Enterprise rescues Picard/Locutus, who they use to destroy the Borg Cube...by telling them all to "go to sleep".
In Star Wars: The Phantom Menace, once Anakin blows up the Trade Federation's control ship, the droid army shuts down.
Also, the Gungan army turns and flees as soon as their shield generator is destroyed. Justified, because the Trade Federation army had brought tanks to the battle, and with the shield down they could move in. And do.
This is still quasi-true in Revenge Of The Sith, given that Anakin is able to shut down the entire droid army after killing the Seperatist leaders. This is largely justified as there was a serious risk of droid rebellion and the controls over those droids were necessary, not to mention that they didn't benefit from leaving their army around if they're already dead.
The earliest Star Wars example is of course the original, with the Death Star's exhaust port. Reused in Return Of The Jedi with the Death Star II's main reactor, not to mention Palpatine dying with it. These both are arguably subversions, however, given that the Empire kicked the rebels off the moon shortly after the Battle of Yavin and that the civil war still officially went on for another fifteen years after Endor.
In the Total Recall 2012 remake, the Big Bad is making an army of robots to take over the only other habitable area in the world. The protagonist finds out about a shutdown code for the army buried in his memories. When La Résistance leader tries to access the memory, this triggers a hidden code that allows the Big Bad to find him. Also played straight when the protagonist destroys the Fall, a gravity elevator from Europe to Australia, destroying the robots aboard.
Literature
Justified in Animorphs. When the heroes take control of the Yeerk Pool Ship and Visser One, the Yeerk general, it provides the Andalite army with comprehensive intelligence on Yeerk military, that allows them to turn tides in the war and defeat the Yeerk Empire.
Zig-zagged in The Chronicles Of Thomas Covenant, specifically The Power that Preserves. Lord Mhoram thinks that by killing Satansfist, the commander of the army besieging Revelstone, he'll be able to route the entire army. It doesn't work, because the ur-vile loremasters take command immediately upon Satansfists death and restore order. But when Covenant defeats Lord Foul, the ur-viles sense it and decide to call it quits, and the whole army crumbles.
In Codex Alera without their Queen the Vord are just animals. Dangerous ones, but manageable. Although normally they possess the ability to give birth to new subsidiary queens, so killing one may rout the Vord in the area, but won't destroy their threat.
The Vord Queen in Alera explicitly says she blocked this ability in all other Vord since other Queens immediately tried to kill her. Of course, this doesn't guarantee what happens after her death
The Buggers and their Queen from Ender's Game. Somewhat subverted in that the Buggers actually know that this is their weakness and actively hide the Queen among the rest of the ships. It takes a genius tactician like Ender to figure out which one is the Queen ship, and even he can't do it in the middle of combat. On top of that, the Queen usually isn't even with her troops, being capable of instantaneous communication from halfway across the galaxy. As a result, Ender ends up having to wipe out whole fleets at a time.
It's played straight in the narration of the past Bug Wars, with the justification that the Buggers only saw killing a Hive Queen as killing, which was part of the reason for Humanity's fear and hatred of the species; when they happened upon a human colony, they dismantled our technology to see how it worked - after they "dismantled" the colonists to see how they worked. They didn't understand how much that would piss us off any more than they could comprehend that we would kill a sentient queen, rather than the nonsentient workers. They've learned.
In the Heralds Of Valdemar series, the kingdom of Hardorn has waged two wars against Valdemar with forces composed of a few mages and loyal generals and a mass of mind-controlled conscripted troops. In both cases, killing the mage freed the soldiers, who then turned on their generals and ripped them to pieces.
In Eragon, the Urgal army in Farthen Dur was routed when Eragon took out Durza, thus breaking his mind control over them.
In J.R.R. Tolkien's The Lord of the Rings, the destruction of the Ring kills Sauron, which confuses and thus incapacitates the parts of his armies which were more directly controlled by his will (e.g. the orcs), which makes them easy game; the not-magically-controlled human armies had various natural reactions, some surrendering and some keeping on fighting.
On a smaller scale, Sauron's human army from Harad are routed when their chieftain is slain by King Théoden.
The Two Towers never does quite explain why the Uruk-Hai turned tail and fled just because The Cavalry had arrived, the film doubly so, since Théoden's men were already surrounded in a sortie while the cavalry were flying into spikes.
Easy reason: Lord of all horses, being ridden by what's basically a pissed off archangel, while a horn loud enough to make a mountain shake is blaring, and being bounced off the walls of the canyon. Urk hai or not, that's going to route you. Add in that any boosts from Saruman were nulled the night before by the Ents.
Not the mention that in the book the force disparity was much less. Rather than battering down the door the the throne room the Uruk-Hai were fighting and failing to take two fortified and entrenched positions, one of which was famous for never, ever falling when they were attacked in the rear by an army more than a quarter of their total.
In the post-Apocalypse novel Malevil, depending on a Keystone Army becomes the plan of attack near the end of the novel. The Bigger Bad is marching his army toward the hero's castle, he rules his men with fear and bad luck has cost him his two best lieutenants. If they can kill him and his last second-in-command then his army should disband. They have to succeed because while he can't take the castle in a single battle, they won't be able to win a prolonged guerrilla war against him.
The Cauldron-Born (an army of undead) from the Prydain Chronicles rampage without end until Taran recovers the Enchanted Sword, Dyrnwyn, and stabs one with it - instantly destroying all of them.
In the Starfire series, the alien Bugs (big spider monsters with insane numbers on their side) are all but invulnerable... until they are stopped by a tiny flaw in their evolution: kill enough of them at once and the others feel the pain of their deaths. Kind of like a whole race of Obi Wan Kenobis, all feeling a billion voices crying out in pain only to be silenced. Only these guys all have a fatal stroke when they feel them.
The Trollocs in The Wheel of Time series are the vicious and terrifying foot soldiers of the Shadow. Unfortunately, though they are violent and bloodthirsty, they are also, by nature, selfish and lazy. The only way they can be utilized effectively as a military force is by having Myrdraal control them with a mental link and the use of fear. This makes them a great danger, but if the Myrdraal dies, so do all the Trollocs linked to it.
In the Doctor Who episode "Doomsday", when the space-time rift that pulled through an army of Cybermen and a ship full of Daleks is closed, it starts to suck them back in.
In "The Age of Steel", the Cybermen are stopped when the program preventing them from feeling emotions is disabled - upon realizing the nature of the Body Horror they've become, the Cybermen kill themselves en masse.
The Ood from "Planet of the Ood" have a form of hive mind. Destroying it would presumably kill all the Oods. The subversion being that the Big Bad tries to destroy it while the Doctor has to save it.
The armies of Vortigern in the 1998 Merlin series. Once Merlin disposes of their king, they cease fighting, and Vortigern's rival Uther is shortly thereafter crowned king.
Music
In the rock opera by The Protomen called "The Father of Death" Dr. Wily, as a Dangerously Genre Savvy Villain, tricks Dr. Light into committing terrorist acts and sacrificing Sniper Joe to destroy his "robot control tower." Turns out Wily has a second control tower located in a fortress and he was only waiting for Dr. Light's attack to give him an excuse to deploy his robot army and declare martial law.
The same goes for the Japanese game of Shogi, which is not unlike Chess.
This is a classic trope for fantasy RPGs like Dungeons & Dragons. Often times the Always Chaotic Evil races of orcs, goblins and trolls are just as apt to fight each other as they are to attack the humans and other goodly races, until a Big Bad manages to terrify them enough into cooperating under his leadership. The evil races' fear of and/or devotion to the Big Bad is all that keeps them cooperating. If the Big Bad is slain, the evil races will just as willingly turn on each other and the army will disintegrate. Needless to say, PCs are typically the ones who are tasked with destroying the Big Bad before his armies can attack the outmatched forces of good.
One of the most notable examples in Dungeons & Dragons takes place in the War of the Lance in the Dragonlance setting. Takhisis, the Queen of Darkness and ruler of the evil gods, keeps her five Dragonarmies united through ruthless discipline and their fear of her. When she is banished back to the Abyss by the PCs, the Dragonarmies turn on each other and begin fighting for power. The canon post-War setting includes five territories that are each held by a mutually hostile Dragonarmy, and are just as apt to fight each other as to attack the forces of good.
This trope actually comes up mechanically in Dungeons and Dragons rather than just from a story point of view. There are several types of monsters who are able to create "spawn" (usually these are undead like vampires and wraiths) and for some of those monsters, those spawn are created completely subservient to their creator. It is possible to build an army of monsters like this, however killing the one who created the spawn in the first place will break the bond of servitude and cause them to act freely. This could be catastrophic for anyone that was using such a monster to create a personal army or just a way to dissipate an army with a single blow.
Probably the inspiration for the Zerg example: The Tyranids in Warhammer 40000 have certain breeds called "Synapse Creatures" that connect lower-tier organisms into the Hive Mind. Killing a local Synapse Creature causes the portion of the Hive under its sway to become disoriented until another one can move in to take its place.
Done literally with the Undead in previous versions of Warhammer, if the general (normally a Necromancer or Vampire) was killed the army would quite literally disintegrate. This was toned down in later editions.
While only mentioned in the fluff, it is generally considered common Warhammer knowledge that killing a major Warboss will inevitably cause any WAAAGH to collpase in on itself, as weaker Warboss' and Orcs start to turn on each other to claim the title, effectively making their horde destroy itself. However, to this troper's knowledge, it does not come into play in a special way in the actual rules.
The spin-off game Warmaster has kill the enemies general as one of the generic win conditions for all armies.
Video Games
Killing the opponent's king unit in Regicide mode in Age Of Empires II gives you instant victory, regardless of how many other units and resources the other player still has. Of course, losing your king will do the same to you. In several campaign scenarios the objective is killing one particular enemy commander or destroying one enemy building too.
In the single-player mode of the early Battlefield series games, your AI teammates are so incompetent that they will constantly lose ground if you're not being Rambo on the front lines next to them.
Subverted at the end of Bad Company 2. Destroying the scalar weapon and killing Kirilenko makes Bad Company think that the Russians will no longer invade the US. Cue a bunch of American tanks rolling up beside them to tell them that the Russians have just started to invade through Alaska.
All the units of the Scrin harvest escort fleet in Command And Conquer 3: Tiberium Wars are powered by Tiberium radiation emanating from a "Relay Node" established at the original Tiberium meteor's crash site, in Italy. While the Node has an operational range that goes as far out as the Moon, its destruction stops every Scrin unit on Earth dead in its tracks, and some even break apart. The Scrin are aware of its importance: it's ludicrously well-defended with everything from stasis shields, Storm Columns and a space fleet to phase fields that render it invulnerable temporarily. Additionally, their original invasion plan called for multiple redundant nodes, but they got sidetracked.
In single player Diablo, all surviving monsters die when Diablo is killed.
In Dragon Age: Origins, killing the Archdemon immediately ends the Blight. Justified since the Archdemon's will is what unites the Always Chaotic Evil Darkspawn hordes into an organized military force. The expansion Awakening subverts this — one of your tasks as the newly appointed Warden Commander in Amaranthine is to investigate why and how Darkspawn are still making fairly organized attacks on the surface (though not on the same scale as a full blown Blight).
This particular Keystone is also much harder to destroy than most examples. Not only is the Archdemon itself incredibly powerful, it can even transfer its soul to the nearest darkspawn and thus be reborn. So unless a Grey Warden sacrifices himself/herself by taking in the Archdemon's soul (an act that destroys both of their souls) or partakes in Morrigan's Ritual which transfers the Archdemon's soul into Morrigan's developing child, the only way to end a Blight would be to kill every darkspawn in existence. Which is impossible considering they outnumber just about everybody and the Broodmothers can generate more at a ridiculous pace.
This is why the first Blight lasted something like two hundred years.
A smaller example occurs in Awakening, where a darkspawn uses a control rod to make a bunch of golems attack you. Killing the darkspawn deactivates all the golems and allows you to loot his control rod, allowing you to use another golem against some darkspawn in the next room.
In every Dynasty Warriors game except for Empires (which has different battlefield mechanics), defeating a general instantly causes his troops' morale to drop permanently to zero and any officers under his command to flee. So if you can get to the generals and put them down (without getting killed, of course), you can quickly swing the battle with a minimum of fighting. There are a number of tasks (particularly in 3) that are nearly impossible to accomplish any other way.
The Elder Scrolls V Skyrim has evil wizards who will often summon up two or more zombies or elemental familiars to fight you. If you kill the wizard, all of their summoned creatures die/vanish. This can comically extend to entire packs of vampires or a dungeon full of necromancers, as they will raise their fallen comrades, who then proceeds to raise more of their comrades. However, if you allow them to do this while keeping track of the last "alive" one, killing him results in the entire room dissipating into dust.
A standard clause for battles in Exit Fate. Even though you and your opponent has multiple units to fight with, as long as you knock out their primary leader, the rest will flee/surrender and you win. (You get a better rating if you take them all out, though.) However, the same goes for you; if the enemy defeats the unit that represents the main character, it's immediate game over.
F.E.A.R.'s Replica Soldiers depend on a psychic commander for their orders and become completely inert when the commander dies. Although this is subverted in the expansions (where Paxton Fettel reactivates them from beyond the grave just a couple hours later) and later games (where another psychic commander and then Alma herself take control of them).
It's mentioned in the backstory of Knights Of The Old Republic II that after the massive amount of death and destruction at Malachor V, Revan decided that turning his enemies into allies was a better idea - and, particularly in the construction of HK-47, this trope was his primary idea on how to accomplish that: kill or convert one influential person, watch everything they held together crumble on its own.
Mass Effect - The Rachni have Hive Queens, who reside on toxic planets. The employment of Krogan (a sentient species that evolved on a Death World, so can survive on Rachni Homeworlds and attack the Hive Queens) was the turning point of the war.
Metal Gear Solid 2 Sons Of Liberty subverts this: Arsenal Gear is designed so that it wouldn't be a keystone if it was ever actually used, because while it's almost invincible as long as it has backup, when it doesn'tit's so weak the Big Bad is willing to leave it to the Quirky Miniboss Squad as a way of killing them off.
The Skedar from Perfect Dark. They had been at war with the Maians for a couple of centuries preceding the game's story, and are only stopped for good when the destruction of their home planet and murder of their king crushes their morale.
One of the bonus missions shows they're Genre Savvy about this to the point that they have three back-up kings ready to take control of their forces in case the one from the main game bites it.
Quite a few RTS will have this as a condition on various campaign levels. The player's goal is to destroy a single unit or structure, and doing so nets a victory, no matter how many enemy units are left on the field.
In Sonic Heroes, there are gold enemies that take all nearby 'bots with them when destroyed.
Justified in a realistic way in the slaughterhouse level of Tom Clancy's Splinter Cell. The bad guys are mercenaries working for cash, and Sam's boss informs him that once he kills their leader/employer, the remaining bad guys will say "screw this" and all go home (since the guy who writes their checks is now dead).
Although it should be noted that if you're in the line of sight of an enemy soldier when you kill this boss, they do continue to shoot at you, which can quickly turn your mission success screen into a mission failed screen, especially since your controls lock up at this point.
The show Burn Notice makes the same remark. Michael points out that if you take out the person handing out paychecks, mooks and mercenaries won't stick around to avenge him.
Something similar happened in The Order of the Stick, when Roy throws Xykon into the portal, he is destroyed. The Goblins in the throne room surrender saying that no one is paying them anymore (though it's more likely that no insanely powerful lich is threatening them anymore). Unfortunately, the goblins tried to surrender to Belkar.
The Zerg in Starcraft are defeated when their Overmind is killed. The Expansion Pack, Brood War, subverts this; without the Overmind to direct their actions, the Swarm launches into a mindless frenzy and slaughters half the Protoss population. Then lots of backstabbing intrigue about control of the Swarm happens.
A similar effect occurs when a Cerebrate is killed, except the Cerebrates only control specific broods, or sections of the swarm.
Note that the Zerg examples are campaign-only. In regular maps, the closest thing there is to a keystone is the Protoss Pylon, which powers all the surrounding Protoss buildings. Take down the Pylons, and the buildings are disabled.
The campaigns themselves are rife with examples where the key to victory against overwhelming odds lies in destroying weak points; for example, "Shatter the Sky", one of the two alternate penultimate missions in Starcraft II, tasks you to destroy a space station with overwhelming forces of zerg crawling on it by taking down its coolant towers.
The Aparoids in Star Fox Assault. As you would expect from a race of giant alien insects, they keep multiplying as long as their queen is still alive. Luckily, they suffer from apoptosis, so killing the queen also kills them all instantly.
In Supreme Commander: Forged Alliance, destroying the Quantum Rift of the Seraphim stops their invasion dead in its tracks.
In both the Supreme Commander game and its expansion, armies will deactivate if their Armored Command Unit is destroyed. In multiplayer mode, losing one's ACU is a condition to lose the game. Justified in that the ACU contains the only person on the field, and that all the other units are robots under his or her control. sACU's are shown to sometimes be piloted by humans, but only in story missions.
The Commander in Total Annihilation is a good example of this trope. If it dies, you lose and your whole army blows up. The same goes for the oppenent.
Occurs twice in the Total War games. First, eliminating the general leading an army causes that army's moral and fighting capacity to decrease, making them much easier to defeat (though it's not an instant win). On the strategic map, removing all the adult male member of a faction's royal family (via Assassination, or by bribing / marrying them into your own faction) causes that faction to lose, no matter how many territory or armies it controls.
Total War also includes an inversion. If a general has a lot of losses, their leadership bonus goes negative. Assassinating a general replaces him with a newly-promoted subordinate who starts at zero. So, killing an enemy's lousy general improves his army's chances for victory.
Subverted in the Warcraft Universe with the Scourge. The only thing keeping the Scourge from becoming an unstoppable army which would consume everything is the Lich King, who controls the entire Scourge and stops them from doing so.
The X-Com series loves this trope. In the first game, the entire alien army is run by a giant brain on Mars. In the second game, the leader is hidden underwater. In the third game, you have to seal off the gates to their dimension.
The third game, Apocalypse, is more of an inversion: In order to seal the gates off, you have to have already destroyed their entire city, and nearly every living thing in it. The gates are the last structure/organism to die.
Given a nod in XCOM Enemy Unknown. After you take an alien base, your Number Two believes that you've broken the invasion. The Head Researcher, however, raises an eyebrow at that, mutters under her breath something about "Too easy", then walks off to begin researching the spoils. She's right. Turns out the base was only an outpost of the main force. Played straight, and Justified, at the end of the game however. Taking out the Uber Ethereal kicks off a reaction that causes the alienTemple Shipto implode, taking the majority of their ships, supplies, and leadership with it.
The Joining from The Batman are an army of robots. They are defeated twice by this: the first time by a self destruct code that had been built into the various parts they were made off. The second time they were defeated by a signal to their mothership ordering them to go offline.
From the same series, an alien army is defeated when the Martian Manhunter frees their power source from the corrupted leader controlling it.
The Kim PossiblemovieSo The Drama has this. Dr. Drakken distributes toy robots around the world which turn out to be giant killer robots that he can activate with a command signal he broadcasts from his headquarters. When he launches the worldwide attack, Kim and Ron foil it by knocking out the main broadcasting tower, causing all the robots to revert back to their harmless toy forms.
Star Wars' use of this trope was lampooned in one of the Robot Chicken specials, where one of the Imperial commanders scoffs at the idea that "The rebels won!", since they do still have a big-ass fleet. Apparently killing the Emperor and destroying the Death Star is enough for the rest to call it a day.
Explained in the books by having Palpatine use the Force to unify his armies to fight more efficiently. With his sudden death, the morale blow of the Death Star being destroyed, and the loss of the fleet commander on the super-star destroyer the Imperial Fleet was thrown in disarray.
Actually, there was one massive reason why the Death Star was crucial. Due to Darth Vader's habit of Force-Choking incompetant underlings, the Death Star had the Empire's best and brightest aboard when iot blew up. Plus, you've just seen the other side blow up a ship the size of a moon. The average Imperial officer is going to think "the rebels have a superweapon, screw this, I'm out of here" not "lucky shot"
A common problem on Ancient Greek battlefields: when the general died, the whole army tended to rout. This was exploited by the Thebans during the Battle of Tegyra. Outnumbered four to one by their Spartan opponents, they went straight for the officers, whose death threw the Spartan army into terminal paralysis.
During WW 2, german snipers managed to take out a fair share of senior officers by aiming for... soldiers with moustaches. Apparently, a british officer could bear to part with his stripes and insignias, but NOT the pride of his upper lip.
Following the events of La Noche Triste, the surviving Spaniards and their Tlaxcaltec allies fled north while being pursued by a far larger Aztec army that cornered them in the plains of Otumba with no possibility of escape. Seeing his enemy weak and outnumbered, the Aztec general Matlatzincatzin followed the Mesoamerican custom, spread his forces and ordered to take as many men alive as possible to sacrifice them back in Tenochtitlan. However, Cortés learned (from the Tlaxcaltecs or from La Malinche, depending of the version) that if he killed the general himself, the Aztecs now deprived of their leader would stop fighting and leave. There was only one chance. Cortés surprised the Aztecs by using his last 23 horses in a cavalry charge that he lead himself, something that the natives had never seen before (they were under the impression, in fact, that horses were only used as pack animals), killed the general and captured his standard. As predicted, the Aztecs broke lines and returned to Tenochtitlan. Cortés then took refuge in Tlaxcala, rebuilt his forces and conquered Tenochtitlan the following year, when the city had just been ravaged by a convenient plague of smallpox.
Football teams can end up like this, particularly if there's a strong quarterback around whom the team's entire offense is built. A prime example of this is the Peyton Manning-era Indianapolis Colts, who were one of the winningest teams in the NFL (even if they did keep fizzling out in the postseason for far too long) until Manning needed neck surgery that took him out of the game for the entire 2011-12 season. After that, they just generally sucked—they were last in the league and won only two games (both late in the season). Fortunately for Indy, they got Andrew Luck—a QB vaguely similar to Manning in style—in the draft for their trouble.
This was especially true of the quarterback-centric offenses of the 1980s and 1990s: after the Joe Montana/Steve Young era ended the San Francisco 49ers returned to being nonentities until this past year. Likewise the Denver Broncos after John Elway's retirement and the Miami Dolphins after Dan Marino's retirement.
If there was one mistake Imagawa Yoshimoto made in his fateful Owari expedition in 1560, that would be his decision have his vanguards separating too far from him central encampment, leaving only about 20% of the troops around him. So when Oda Nobunaga staged a surprise desperate attack on Yoshimoto's own encampment, Yoshimoto was quickly overwhelmed and killed, propelling Oda as a front-running daimyos of the era and tarnished Yoshimoto's image. The latter is generally seen as incompetent only because of this Battle of Okehazama.
This is part of #18 of The Thirty-Six Stratagems - if your opponent's foot soldiers are in it only for the paycheck, taking out their leader means they will fall away and be of no threat to you (or possibly even join you, if you have money). However, the other part of this stratagem warns that if they're loyal to the commander because of his character or some ideal, taking him out may inspire them to fight harder, so it's important to discern correctly their reasons for fighting.
While the battle of the Alamo was an eventual loss, the damage inflicted on the attacking army was so intense because the leaders wore decorative hats, which made them a primary sniper target. One of the reason why the leaders of armies today don't have much to separate them from their troops.
The Battle of San Jacinto was won by the outnumbered Texas Militia by attacking Santa Anna's camp, and the entire war was ended when Santa Anna himself was captured shortly afterwards.
