Alice: Madness Returns has 'Hysteria Mode', which is activated when Alice's health is down to one rose. Time slows down and she is able to deal more damage to enemies. However, it only lasts for a short while.
Castlevania: Aria of Sorrow has the Lubricant soul, which raises your stats as your health drops. It also has the helpful item spoilt milk, which drops your health to one.
In The Incredible Hulk: Ultimate Destruction, when Hulk's main life bar is depleted, he enters Adrenaline Rush mode, which reveals the last of his life, increases his strength and gives him unlimited Critical Attacks. It's not easy to get or maintain an Adrenaline Rush as Hulk will regenerate to 75% of his main life bar when he's not getting hit and gets health from any enemy he defeats, meaning any situation that puts him into it will likely kill him before he can use a Critical Attack.
In The Minish Cap Link learns, in addition to his normal full-health Sword Beam, a beam attack that only works when his health is at or below 1 heart.
One of the few things most Devil May Cry fans admit to liking about the otherwise non-existentDevil May Cry 2 was the Desperation Devil Trigger. When Dante's health was in the critical, activating his Devil Trigger Super Mode would cause Dante to shift into a towering alternate devil form with Nigh-Invulnerability and dramatically improved power.
In Ninja Gaiden, the Unlabored Flawlessness becomes the most powerful weapon in the game if your health is at critical levels.
In Ninja Gaiden III and Sigma+ on the Playstation Vita you get the option for "Hero Mode" which activates at 30% or less health and makes guarding and evading automatic, rendering death almost impossible, and last for a fairly long time.
Art of Fighting introduced the Desperation Move, which can only be used when the player's health is under about 1/3rd. This was retained in future SNK Fighting Games.
Dead or Alive 5 has the Power Blow, a move that, if it connects, unleashes a cinematic combo and ends with you aiming where you want to launch your opponent, like into a stage hazard or off an edge. What makes it a Desperation Attack is that it can only be used when you're below half health.
In the Dragon Ball Z Budokai games, there are several ability capsules you can equip that activate when your health drops below a certain point. Character-specific examples are Babidi's Mind Control for Vegeta (Turns into Majin Vegeta when health is at one bar or less) and Frieza's Space Ship for Frieza or Cooler's Space Ship for Cooler (Turns into Mecha Frieza or Metal Cooler respectively when health drops to zero). Other examples include Senzu Bean (Restores health to full when health drops to zero) and Senzu Bean 1/3 (Gives you an extra bar of health when health drops to zero).
Dragon Ball Z: Hyper Dimension for the Super Famicom had actual desperation attacks for the characters, which could be used when the characters health dropped to a certain amount.
In the doujin Fighting GameEternal Fighter Zero, each character has a unique "Final Memory" move, which is a level 3 super that is only accessible when the character is down to their last 1/3 health. These range from extremely damaging attacks to special effects like freezing time or granting hyper armor. In many cases, the attack models the canon scene in which the character dies, hence the name.
Fatal Fury was also one of the first and most well-known uses of the trope.
Later, this mechanic disappeared, so supers were Desperation Moves only in name. However, these returned in The King of Fighters 2002 and its Unlimited Match remake. In these games, a character's MAX2/Hidden Super Desperation Move can only be executed with 3 super bars and 35% health or less.
Some minor SNK games (and certain Grooves in Capcom vs. SNK) would allow the player to perform unlimited Supers if their health was critical.
Magical Battle Arena combines this with the Super Mode mechanism. A few of these moves, however, inflict damage on the user, which is a bad thing since you have to be on your sixth and final bar of health in order to use the attack in the first place.
In Marvel vs. Capcom 2: New Age Of Heroes, if Jin was the last member alive on a team with less than 30% health left, he activates Golden Super Mode upon standing on the ground. It takes two hits to stun him, his attacks are strengthened and specials augmented. However, if an opponent can keep him off the ground, he can't activate it.
In Marvel vs. Capcom 3, knocking out Phoenix with the super meter at le-le-le-le-MAXIMUM fully heals her, turns her into Dark Phoenix, and provides her an enhanced moveset. This health is meant to be balanced, as: Phoenix and Dark Phoenix each have 420,000 hp (the lowest for any other character, including resident Glass Cannon Akuma, is 800,000); the pair have pitiful defense; and Dark Phoenix's health drains constantly (though it alone can't knock her out). The two of them do have a Healing Field super, but it's very short-ranged and so either powerful or punishable.
3 introduces the X-Factor ability, which is available to everyone on the cast, although the actual effect is unique to each character. It can be triggered at any time but is best used as a Desperation Attack because the fewer characters you have, the stronger and longer the effect.
In Persona 4 Arena, all characters enter "Awakening" mode upon breaking out of a combo with 35% of their health left or lower, granting increased defense, 50 SP, and a new SP attack, which is in arguably every case, their strongest attack. (outside of the Instant Kill moves.)
Samurai Shodown 5 had a mechanic called Mu no Kyouchi ("Circumstance of Nothing"), which caused the opponent to slow down and opened up a powerful attack, but which could only be accessed after one already lost a round and had lost a certain level of health. Also inverted with the game's finishing attacks, which only worked if the opponent had already lost a round and a certain amount of health.
In Super Smash Bros. Brawl, Lucario's attacks get more powerful as his damage percentage increases, peaking out at 168%. This is invoked in an event match where you have to play as Lucario starting out with high percent (182%).
Related: If a character is down several points or stock, they automatically gain Final Smash powers the next time they drop down onto the stage.
Tekken 6 has "Rage Mode", which activates when a player is near death, making them much stronger.
Also a case of The Computer Is a Cheating Bastard, as in arcade mode, and most modes, in fact, when you fight Jin, at the start of every round he will begin in Rage Mode. Even worse, the true final boss gets an upgraded Rage Mode, where both attack and defense increase dramatically. And it's also activated at the beginning of the round.
In Borderlands 2, Krieg has a skill called "Light the Fuse" that makes it so that when his health reaches zero, rather than being forced to his knees and hip-firing, he instead breaks out a bundle of dynamite and becomes a Suicide Psycho. In this state, he can freely run around and chase down enemies while tossing dynamite at them. When the timer runs out or if you trigger it, he'll then blow himself up. If he manages to score a kill, he'll earn a Second Wind and be back to normal (though killing enemies by suicide bombing them earns him a temporary speed boost).
Most of the skills in his "Mania" skill tree is about dealing as much damage as he takes. His most powerful skill, "Release The Beast" lets him transform into a Badass Psycho when he's at 33% health.
In Team Fortress 2, the Soldier's Equalizer is meant for this. Initially, it would not only increase in power the lower his health, but also allow him to run faster. Since the weapon has been split into two different weapons, one dedicated to each of the original's bonuses, the new Equalizer is now solely dedicated to this. On top of this, the weapon blocks healing from Medics, making it even more of a desperation attack. Finally, as a last resort, the Equalizer reaches its ultimate in its desperation. As a last ditch effort, the Soldier can toss it away, then use one of his grenades to blow himself up, along with any enemies and buildings within six feet of him.
Both the Dynasty Warriors and Samurai Warriors games have Musou attacks, Limit Breaks that build by attacking and getting hit. However, if your character is at red health, the Musou meter will fill up on its own over time and the attack will come in the form of a stronger version called a "True Musou".
City of Heroes gave the Blaster archetype the inherent ability of Defiance, which raises their attack power as their health drops (as of the eleventh update, this is no longer true—Defiance in that form was widely considered to be useless at best, and actively detrimental at worst by encouraging stupid play—so it was retconned into a more widely useable form). Defenders also get a desperation power called Vigilance, which reduces the endurance cost of their powers as their teammates' health drops (and this is also generally considered quite useless, as it 'rewards' you for doing your job badly, so a good player is unlikely to ever see this benefit).
Amusingly, Defiance was originally called "Desperation" during beta testing of the update it was added in, but the name was changed due to player complaints. Considering how useless the original version of it was, it remained known as Desperation amongst players until it was finally upgraded.
Vigilance was better than Defiance, in that it's more practical to keep a mixed (or all-Defender) team at a specific percentage of health than a single Glass Cannon, and most Defenders had more productive things to be doing with their powers in many situations than keeping teammates at full health. Unfortunately, a team competent and organized enough to take advantage of Vigilance didn't actually need it, so the concept remained mostly undeveloped.
Dungeon Fighter Online's Asura's have the Deadly Enticer skill. While the requirement doesn't specify that they must be at low health, they have to have taken a certain amount of hits, and the most practical application is to use it when caught in an opponents Spam Attack which is usually going to be lethal
In Guild Wars, an elite Necromancer skill stole enough health from a target enemy to bring your own to 50%. Though double-edged (it could lower your health, and heal the enemy if used when you were above 50%), and originally intended as an "oh $(@#" skill, it was rarely used that way. The skill was used to destroy some otherwise very difficult bosses by pumping the Necromancer's max health as high as possible, having the Necro hurt themselves down to very low health, then hitting this skill to tear away a big chunk of a boss's health.
In The Lord of the Rings Online, the Warden class has a single skill that restores power, which is needed to execute skills. However, this skill can only be used when the Warden has less than half of its health remaining. This is an interesting case, since the Warden also has a few skills that heal itself. This means that as long as the Warden doesn't heal itself too much, it can find a balance between regaining health and regaining power, allowing them to stay in a fight where other classes would eventually run out of health or power. This technique, known on the forums as "morale-surfing", essentially comes down to relying on your Desperation Attack to keep you from dying, while slowly burning down your opponent.
In RuneScape, the full Dharok's armor set has the effect of increasing the maximum hit when all four parts (helm, platebody, platelets, greataxe) are worn and remaining life points are low. As this armor degrades if dropped on death, players will often enter safe minigames (where nothing is dropped on death), and intentionally reduce their health to near-zero in order to inflict massive damage and gain massive XP. A favorite trick of players who train combat with this armor is to get one's health extremely low, then activate a protection prayer to stop damage, keeping him or her locked in desperation mode.
Star Trek Online Has the ability "Go down Fighting" which allows the player to do more damage the lower their ship's hull condition is.
World of Warcraft: The troll racial ability Berserk used to be stronger at low health.
The Warlock class has a talent that increase the effect of their Drain Life spell when their health is below 30%.
Many boss encounters are more dangerous at low health due to this.
Honorable mention goes for this quote: "So much unstable energy... but worth the risk to destroy you!"
In a tactical sense, if a party is wiping with the boss at low health some players may use self-resurrection abilities just to get in a few extra seconds of damage.
The Skeleton Pirate boss in Binary Boy can only attack by shooting scripted cannonball sequences from the background. He begins with eight cannonballs that are easily dodged, but their number doubles with each successful hit on the shipwreck you need to destroy to win the battle. By the end of the battle, he'll fire about 60 of them.
Iji has the Retribution technique. You can only activate it when Iji's health is 5 or below and you have all 8 basic weapons, plus it only works once per area/boss. Still, it comes in handy for when you really want to dish out the hurt. As a bonus, it's also an Invulnerable Attack.
All the first 8 bosses of the Mega Man X series starting from X2 gain one on low health. These generally do a lot of damage to the player (Crush Crawfish's Bum Rush, Bamboo Pandamonium's Youdantotsu), or put him in an undesirable situation (Wheel Gator drills spikes into a wall, Blizzard Buffalo fires a Freeze Ray).
In X8, all of the first 8 bosses' Desperation Attacks are also used by the first form of Lumine.
Six of the first eight bosses in Mega Mari have these. A notable one is Reimu's, which continually spawns high damaging yin yang orbs until defeat. The orbs (and most attacks for that matter) can kill you even after the boss dies as well.
The Binding of Isaac has Whore of Babylon item which Eve starts with. When health drops to half a normal heart, the player turns into a demonic form with greatly increased damage which lasts as long as the player exits the room with half a normal heart. One strategy is to get an item which slowly refills soul hearts and use a Blood Bank to get down to half a normal heart to keep this ability going. This item is not a desperation attack for one of the unlockable characters, though: when he picks it up, the effect is permanent.
In Leagueof Legends, there are several champions who get their stats boosted as they take damage. Olaf gains attack speed, Tryndamere gains bonus damage, and Aatrox heals himself more. Poppy's innate ability will typically cause her to take less damage the lower her health is. There is also an item called Maw of Malmortius that gives more attack damage the lower your health is. In fact, Maw is only cost-efficient when you you are low on health, stat-wise.
Star Wars: Empire at War and its expansion have, for some units, the ability to self-destruct. The TIE Mauler was the only one to have this in the first game, and considering how pathetically weak its armour is, the self-destruct became useless unless the player managed to park ten of them at full health in the middle of an enemy formation first, just to ensure that at least ONE did some damage. The expansion gives this ability to the following Zann Consortium units: MZ-8 Pulse Cannon tank, Vengeance-Class Frigate, Aggressor-Class Destroyer. Much more effective for them since a. It's automatic and b. those units could actually survive long enough after taking a shitload of damage for the ability to be effective.
In the popular Warcraft 3 map Defense of the Ancients: All-Stars, Terrorblade the Soul Keeper has the Sunder move that swaps his health percentage with a target's, naturally becoming stronger as he gets weaker. Huskar the Sacred Warrior has Berserker's Blood, which increases his damage and attack speed as he takes damage, but only increases in power down to 58% health. Abaddon the Lord of Avernus has a variant in his Borrowed Time move, which turns any damage taken into healing while active, and can auto-activate if he drops below 400 hp and it's available.
Breath of Fire has your characters attack faster when their health points are dwindling.
The Crisis Arm, one of Robo's final weapons from Chrono Trigger, claims to work this way, but actually depends on the last digit of your HP. There are actual desperation attacks in the form of Frog's "Frog Squash" tech and Ayla's "Dino Tail" tech.
Then, there's the Combination Attack Grand Dream, which is a massive, impressive three-character Desperation Attack. It's surprisingly effective against the final boss, simply because he has a habit of near-flattening you. Grand Dream contains Frog Squash as one of its components.
The similarly insane Frog Flare (a Combination Attack of Frog Squash and Lucca's * Flare) is universally acknowledged to be the best way to take out the final form of Spekkio, who uses Hallation a lot - particularly if you're playing the DS version and got the Game Breaker armor for Lucca, which renders Hallation Spekkio's only attack capable of damaging her - and you're never going to die from HP to One attacks.
Fenris from Dragon Age II has the Veneer of Calm ability, allowing him to do increased damage as his health drops.
This ability is also on the Ravager talent tree somewhere.
The Hexer's Revenge ability in Etrian Odyssey is straight defense-ignoring damage based on how little HP the Hexer has remaining. It was toned up and made even more powerful in the sequel.
The Fallout series of games have a few perks that reflect this ability, such as Adrenaline Rush (raising your strength if you drop below 50% hp), Die Hard (raising resistances to damage when you drop below 25% hp), and Nerd Rage! (increasing your strength to maximum if you dropped below 25% hit points—and requiring a certain amount of Science skill).
Unfortunately, by that stage of any of the games, your character was likely to be wearing items boosting strength to 10 (absolute maximum, no temporary bumps over it allowed), or 8-9 if the starting build was really puny. Add to that the fact that the most successful melee and unarmed builds only required and effectively used medium strength scores, and it really seems pointless (melee and unarmed being the only usable attacks utilizing strength score bonuses, only other uses of strength were max carry weight and min score to wield weapon, as well as the really rare and optional quest and the absolutely buggy and random throw skill). Also, unlike Dungeons&Dragons, strength bonuses were small and rather linear, with the average weapon in the second half of a game dealing 10 or 20 times more base damage than the strength bonus. Furthermore, since enemies were plentiful and came in groups, which were defeated by a combination of strategy and predictable/expected critical hits, these strength bonuses really meant nothing whatsoever. A temporary increase in carry weight, only in the heat of battle and at the brink of death, also obviously provided little benefit in a world without encumbrance-increasing magic.
Final Fantasy V, has a Blue Magic spell called ??? (which actually has nocall box). It does damage equal to the difference between the user's max HP and current HP. Therefore, using it when you're at critical HP will do damage almost equal to your max HP. It shows up in many other Final Fantasy games after V, as a Blue Magic spell, either named "???" or "Revenge/Revenger/Revenge Blast". However, it's a bit of a Useless Useful Spell, as enemies who have the move tend to have max HP many times higher than what you ever get, making it a potential One-Hit Kill in their hands.
Final Fantasy VI introduced actual Desperation Attacks to the series, incredibly powerful attacks that can randomly occur when a character with critically low HP is given the "Fight" command. However, they have only a one in sixteen chance of occurring, meaning most players don't ever see one. There is also the Valiant Knife, whose power increases as the wielder's HP decreases, making it the opposite of the Ultima Weapon, which gets stronger the more health one has.
Final Fantasy VIII's Limit Breaks. The availability of the Limit Breaks is predicated on how much HP there is left proportional to your total HP, so if your health stats were high, which is easy to accomplish even early in the game with proper junctioning, you'd still be able to access your Limit Breaks with a reasonable number of HP. The game lets you know exactly when you can use them by turning the stat display yellow, and you can reset the Attack option an unlimited number of times per turn with the circle button until it gives you the option to use your Limit. This feature makes them your primary mode of attack, not a desperation attack, and all but renders them Gamebreakers.
Final Fantasy IX has Steiner's Revenge ability, as well as his Charge!, which causes every other party member at low HP to use their normal attack without using up their turn.
And the Blue Magic Limit Glove, an otherwise unremarkable spell which is guaranteed to do 9999 damage if (and only if) Quina has exactly 1 HP left when using it. Mostly useless because of this limitation, but with proper element cancellation...
The standard strategy is to give him/her Auto-Revive, and then let something kill him/her - which brings him/her back on 1 HP. Failing that, Phoenix Downs are close to useless for all other purposes, because they only provide single-digit HP; however, that means there's a one in nine chance...
A lot riskier and more luck-based, but if one of Necron, the final boss's, attacks reduces one character to 1 HP. However, that both requires Quina to be the target, as well as Necron not launching a follow-up attack that does any measure of damage to Quina.
Savvy players will knock Quina out in a battle, then go to a save point and revive him/her repeatedly (resetting each time) until s/he has 1 HP. Perfect for taking out that tricky boss in one shot! It's also available extremely early (from the moment you get Quina, in fact), letting you lay the smackdown on the rest of disc 1 and most of disc 2 (by disc 3 more reliable means of violence become available). By extension, it's also a valuable skill to have when doing the Excalibur II challenge.
Several items in Final Fantasy XI, such as the Sorcerer's Ring or the Rasetsu armor set, have effects that only activate when the wearer's HP drops below a certain percentage.
Final Fantasy Tactics has the Meatbone Slash Reaction Ability, which deals your max HP in damage when your HP is critically low. It also has several other Reaction Abilities that function on the "Critical HP" principle, usually bestowing healing or auto-life effects. Finally, there are several attacks that utilize differences in your HP or MP to do damage.
In addition, several of the games have skills that do a set amount of damage equal to a character's maximum HP minus their current HP.
In a diversion from the usual Limit Break method of dealing with this for the series, Final Fantasy XII allows you to combo attack much more frequently the lower your health. One of the best methods for dealing with most of the Bonus Boss's uses this to its advantage by berserking 2 of your characters in critical health while using the third as a decoy.
Final Fantasy Tactics A2 has the Blue Magic spell Cornered/Limit Glove, mostly used by Rockbeasts, which does 999 damage if the user has single-digit HP. Auto-revive is needed to learn it, since one must survive the hit. Amusingly, the AI will try to use the attack once they reach critical HP, even if their health is still too high for the attack to have any effect.
Dissidia: Final Fantasy has a variant of this with the Cosmos Judgment rules. When a player is in danger of dying in one more hit, their EX Gauge will instantly max out, giving them a chance to turn things around.
There's also the equippable support ability 'Back to the Wall' (which increases the player character's critical hit rate when their HP is in the red). 'Cat Nip' (which increases the player character's critical hit rate when they're at risk of losing in one HP attack) can often count as this as well, but the nature of the battle system means that the attacker can potentially win with one HP attack regardless, assuming their BRV gets high enough to allow this.
Kingdom Hearts II has two of these, in the form of equippable abilities. One is called "Crisis Half" which halves any damage when your hitpoints are below 25%, the other is "Exp+" which gives double EXP.
Considering that this is Final Mix+, those two really help with the Critical Mode.
The original game and midquel have the ability Berserk, which does indeed increase attack at critical health levels (the latter game and its remake requiring the use of the Hades enemy card).
358/2 Days has the Limit Breaks, which can only be activated once your HP falls to 25% (50% with the right panel equipped). However, the threshold keeps getting smaller with each use, making each Limit Break riskier than the last.
All the same, as they can create a nearly minute-long attack that can deal upwards of hundreds of times your normal damage output, they will often be your method of choice for dispatching tough enemies. That said, the effects—and therefore the effectiveness—differ from character-to-character. Some have to charge, while some just go berserk, some hit in a radius around them, some only strike forward, some are granted temporary invincibility, some are frozen in place, etc.
Atton Rand from Knights of the Old Republic II has "Fighting Spirit," which causes his saving throws to increase as he takes more damage.
Paper Mario has a couple badges that only kick in when Mario is down to 5 HP or less, such as Power Rush, which boosts Mario's attack power by 2. Then there's Mega Rush, which boosts Mario's attack power by 4 (increased to 5 in the sequel) but only when Mario has exactly 1 HP left. Paper Mario: The Thousand-Year Door also allows you to obtain and equip multiple Power Rush badges to stack their effects, although damage is capped at 99 per hit.
Flail and Reversal are moves that get stronger the weaker the user is. When the user's HP are at less than 4% of maximum, these moves do the most damage.
Pain Split divides your current HP and your enemy's current HP evenly between you; the more HP than you your opponent has, the better.
Endeavor lowers the enemy's current HP to match your own.
The moves Eruption and Water Spout are inversions: they get stronger while the user's HP is near maximum.
On other hand, the move Brine does more damage if the user's HP is below 50%.
Last Resort is a powerful move but can only be used if all the other moves the user knows have ran out of PP.
The Guts ability dramatically increases strength if the user has a status ailment, while the Marvel Scale ability improves defense under the same circumstances. A bit more specifically, the Tangled Feet ability doubles evasiveness if the user is confused.
Quick Feet is Guts/Marvel Scale for speed.
Facade is Guts turned into a move.
Overheat, Psycho Boost,Draco Meteor and Leaf Storm sharply reduce the user's Special Attack level, making them less and less powerful the more times it is used. Superpower and Close Combat are variations of this; they are slightly less powerful, but lowers the user's Physical Defense as well as another stat (Physical Attack for Superpower, Special Defense for Close Combat).
Struggle is an Emergency Weapon (and Cast from Hit Points at that), as it only executes when the Pokemon has run out of normal combat moves. It also comes into play if the opponent's Pokemon has used Encore, thus blocking the player's Pokemon from using any moves other than the one it last used, and that move is out of PP. It is completely exempt from the usual Elemental Rock-Paper-Scissors.
Tales of Symphonia has the Over Limit form which cuts damage in half and prevents the character from flinching when hit. It activates when a character's invisible Tension gauge is filled, which can be done in many ways, but the one you'll probably fill it up with the most is taking damage. Or cooking.
Also, Lloyd's Falcon Crest, his deadliest attack, can only be used when his health is at 16% or less. In addition, Sheena's most powerful techs, the Summon Spirits, can only be performed while she is in Over Limit mode (Double desperation?).
Most of the other characters can also only use their most powerful attack when in Overlimit or at low HP. The most extreme example is Presea in the Updated Re-releasePS2 version, who requires everyone else to be knocked out and her to be at critical health and even then whether or not the move activates is random, but to balance it out, it's by far the strongest attack in the game.
Wild ARMs 3 has Valiant, a spell that adds the difference between the recipient's current and max HP to their attack power.
A number of clothes in The World Ends with You have abilities called "SOS", which only trigger when the player is in "mortal peril" (their health bar is completely off one screen and less than half is left on the other).
Later in the story you can use the Lapin Angelique Suicide Special (LASS) strategy, which puts you in mortal peril at the start of battle. As the name suggests, all the gear you need is from the Lapin Angelique line, which tends to be oriented towards this trope anyways.
Xenogears has an equippable item which increases your attack power ridiculously when near death. If you give it to Fei, he can do 19998 damage every turn when not inside his Gear... and being outside his gear means most of the time gear-sized enemies miss him. He becomes a gear-destroying machine.
There's a similar accessory in the Spiritual SuccessorXenosaga Episode 1 called the Bravesoul. It increases the equipped character's attack power as their health falls, leading to noticeable bonuses at half health, and a situation reminiscent of a Final Fantasy VIIILimit Break-fest at critical health.
Disgaea 2 is rife with this, some characters getting random 1-Hit-Kills, Double Attacks, or stat boosts at 25% health. To help with this, you can equip an accessory that limits your HP to 25%.
Fire Emblem 9 and 10 have several abilities that improve stats when health is below a certain amount or percentage, usually only available to player characters and bosses.
In a similar vein, Fire Emblem 4 has the skills "Wrath" and "Ambush", which activate when a character drops below 50% health, giving automatic critical hits and first strike, respectively. And "Prayer," which activates in the low single digits and greatly increased evasion.
Fire Emblem Awakening brings back Wrath (nerfed to +20% critical chance at half health) and Ambush (now Vantage).
In the Super Robot Wars games, this happens if a pilot has the "Prevail" skill. Once a certain percentage of their HP has been depleted, they gain major stat boosts.
In any Total War game, if a unit breaks and is unable to flee, it goes into "Fight to the Death" mood, boosting the unit's attack.
When your momentum gauge flatlines in WWE Day of Reckoning 2, you gain access to a powerful Momentum Shift attack, which swaps your and your target's momentum gauges.
In WWE '12 a character can have the "Comeback" ability. This allows a severely damaged character to get up and/or launch a flurry of attacks in a quick-time event which leaves the character's momentum gauge full and their opponent dazed, ready for a Finishing Move.
In The Art of War, Sun Tzu warns against a combination of this and Last Stand. "Throw the troops into a position from which there is no escape, and even when faced with death they will not flee." In actuality, Sun Tzu was warning against this because desperation attacks can still be pretty effective even if the enemy dies while doing it; that is, if someone dies but takes out a decent chunk of your infantry while doing so, they've still won since you need time and man power to replenish and must potentially stop your forward progress. His answer was to always leave an escape route for the enemy, thus allowing them to rout, making them easy targets... and allowing them to run into the ambush you set up on the escape route so you could take them out there.
In modern amphibious assaults, this was one reason for their success. The attacking soldiers have nowhere else to go and so they have no choice but attack directly.
Exalted: a number of Malfeas Charms actually become nastier as your wound penalty increases, such as the Parry DV penalty reducer, which starts providing more bonuses as you take more injuries (that don't cause penalties because Feel No Pain is a major part of the Malfeas charmset). The most impressive, however, has to be Driven Beyond Death, which allows you to respond to being killed by going full-on One-Winged Angel.
In sports where points are gained by scoring goals, a team that only needs one goal late (generally Football variations) in the game will send their goalkeeper to attack especially from corners. It's very risky as it leaves an open goal but when it works, it works well. The FIFA games in particular have implemented this behaviour for since '08. Down to the Last Play has more examples of when this comes off.
A less extreme but still risky version of this is if a team has a tall defender, they will often be sent to play up front of the attack as a target man. The team will attempt to punt, cross or lob the ball in a way that the defender can score a headed goal or knock the ball down to a team-mate. An example of the tactic is that Manchester United will often send their central defender Nemanja Vidic up front if they are down towards the end of the game.
An inversion of this tactic is when a team's attack has tall forwards who play the entire game as 'target men'. This is generally called the "long ball" tactic and considered to be a lower skilled and non-technical style that is often utilised by teams of inferior skill to others. It is often utilised in lower divisions where fast and technically skilled players are rare but physically strong and tall players are common.
Ice Hockey has the tactic of 'pulling' the Goalie, where the goalie leaves the rink and is replaced by a non-goalkeeper. The few occasions that a Goalkeeper has scored in the NHL, it was as a result of the other team pulling their goalkeeper and leaving an empty net. It has also led to a handful of embarrassing own goals by misplaced passes or a player being unaware the goalkeeper wasn't going to be there to receive the pass. It's statistically a goal-losing proposition (in the NHL, empty-net situations with a one-goal difference at the end of a game on average sees the team in the lead score a goal about 1/3 of the time and the team behind score just 1/9 of the time), but regardless of the margin of victory a loss is a loss.
There is a inversion in Australian Rules Football. At the end of a match where a team is down by a few points, if they receive a mark or free kick both teams will 'flood' their entire team towards the goal area. The inversion is that it's not the attacking team which causes this, but the defending team who seek to cause as much disruption as possible to any attempt to catch the ball which can result in a free kick at goal. If the defending team does not flood back, it is better for the attacking team who would prefer the open space for their attackers to use to run onto a ball or jump to catch it. When they do, the attacking team has nothing to do but send all their players forward to try to counter the numbers of defenders. It is a desperation defense which the other team will then turn into a Desperation Attack.
In a sort of meta-example, there is this famous comeback video of a Street Fighter III match between two high-ranked players. The comeback was not the result of a desperation attack, but by the skillful application of another game mechanic built into the game in the context of a situation which would have called for a desperation attack had one been implemented into the game.
In gridiron football, the quarter does not end until the clock expires AND the ball is dead. Therefore, it is always possible to score a touchdown on a single play. With seconds remaining in the 4th quarter, a team down by a 4-8 points (or by 1-3 but out of field goal range) will execute one of two plays to try to score in one play: the Hail Mary Pass, which calls for five wide receivers breaking for the endzone while the quarterback throws up a jump ball, or the Hook and Lateral, wherein the quarterback throws a short to medium range pass, and then the offense attempts to cobble together broken field runs and lateral passes to keep the play alive until they score. Also, since the half cannot end on a defensive foul, if the defense commits a penalty on such a play, the yardage is applied and the offense gets a free play. A defensive pass interference on a Hail Mary Pass gives the offense one play from the 1-yard line.
Another desperation play in the onside kick, in which the team kicking off attempts to recover the ball after it has traveled ten yards down field or been touched by an opposing player. Usually, it's used when the kicking team is trailing without sufficient time to get the ball back by playing defense, but it's also occasionally used as a trick play at the start of a half. It has about a 10% success rate, in part because the receiving team is usually expecting it and in part because the receiving team doesn't actually have to recover it- they just need to prevent the kicking team from recovering it — if the ball goes out of bounds or is touched first by the kicking team within ten yards of the kick, the ball goes over to the receiving team. (Unexpected onside kicks do have higher success rates, though the rate goes up to about 33% and a team doing it too often makes it no longer unexpected.)
The famous Scott Smith/Pete Sell fight in the UFC featured Smith taking a direct hit to the liver which, for those who don't know, basically puts you on a very short timer before temporary paralysis sets in. While Sell moved in for an entirely-unnecessary follow-up, Smith threw one last punch. Sell, naturally, thought he'd already won, so he'd dropped his defence. Then this happened.◊ Smith's not faking there; immediately after that moment he collapsed too.
In basketball, a missed final free throw on shooting and floor fouls is live, so a team down by 2-3 with one free throw remaining and only a few seconds left on the clock will attempt to miss the free throw and recover the rebound for a chance at a field goal to tie the game. This has a success rate similar to onside kicks in gridiron football.
Baseball imposes no restriction on defensive formations beyond needing to have a pitcher on the mound and a catcher behind home plate. Thus, on rare occasions where the winning run is on third with fewer than two outs, the center fielder may come all the way in to second base to serve as an extra infielder.