InuYasha's Bakuryuuha (Backlash Wave) fits, since it turns an opponent's ranged attack back upon him and the opponent's aura has to be weaker than InuYasha's.
Earlier in the series, the Kaze-no-Kizu (Wind Scar) can only be used if Inuyasha can find the "rift" between his aura and the opponent's, and cut through it. Make particularly difficult by Kagura, who can control wind and thus manipulates the flow of their auras so Inuyasha can't find the rift.
Attack on Titan features Eren Jaegar, whose ability to turn into a Titan only activates when he's injured. However, he instinctively realizes that self-harm works as well, and from then on it becomes a controlled ability.
In Dragon Ball Z, the requirements to activate the Saiyan Super Mode are similar to this. Once a Saiyan of sufficient power has been pushed over the Despair Event Horizon, said Saiyan will trigger the golden-haired Super Saiyan state. Part of Gohan's training involved taking control of his anger in this fashion.
Majin Buu's Angry Explosion also fits this trope, as it's only activation is when his massive anger is triggered.
Tengen Toppa Gurren Lagann's GIGA DRILL BREAKER can only be unleashed when the main characters spiral energy peaks (usually caused by an extreme burst of emotion).
In Gurren-Lagann The Satire, when Simon and Kamina use Giga Drill Break, Kamina doesn't shout FINISHING MOOOOOOOOVE! Instead, he actually shouts "LIMIIIT BREEEEEEEAK! GIGA DRILL BREEEEEEEAK!" This is despite the series trying to avoid tropes and main-stream pop-culture references.
Naruto does this as traditionally as Dragonball. Naruto's first activation of the Nine-Tails Chakra occurs after believing that his friend/rival has been killed, enraging him and tapping into his hidden power. Eventually Naruto learns how to activate this power at will, so it's not really a Limit Break anymore. Prior to this, though, it manifested primarily when Naruto saw his friends being injured or killed, ironically, in one incident, this actually caused further harm to his own team.)
In One Piece, Luffy's first use of the Gears is considered a Limit Break, especially Gear Third. So much so that Gear Third shrinks him down to a small, kid-like chibi form (Before the timeskip, anyway). Gear Second, on the other hand, is Cast from Hit Points.
Shinji of Neon Genesis Evangelion can trigger one when he's under extreme emotional duress, whether from battle fatigue or just sheer pressure. His EVA 01 unit goes berserk in a scene usually complete with horror. Unit 01 goes berserk whenever Shinji's life is in danger to the point that he's almost pissing himself in fear. The other, much more powerful kind appeared in the second Rebuild movie and was triggered by his Berserk Button; as such, his opponent is completely fucked. In fact, him going full-power had triggered literally The End of the World as We Know It and turned Unit 01 into a Physical God by vaporizing it's Restraining Bolts. In the same movie, Mari was able to manually activate and control EVA 02's limit break by disabling its Restraining Bolts.
The eponymous Sekirei have a form of this. A special power-up and attack available only when their Ashakabi kiss them of all things.
A variation is used in Hellsing. As Alucard's powers are controlled by Integra via Hermetic Magic, only she can say how much of his power can be used. This is seen when different levels of Alucard's power are released, culminating in the Godzilla Threshold when Alucard's full power is unloaded, allowing him to call forth the thousands of souls he has consumed over the years to tear the forces of Millenium to shreds.
In Bleach omakes and anime, it's revealed that Hanatarou's zanpakutou is this, absorbing the injuries of others that fills a gauge on the side of the sword whereupon the stored power can be used as a surprisingly powerful, explosive attack.
Rukia's third dance can only be used when her zanpakutou has broken.
Renji's shikai can also perform a special manoeuvre (Higa Zekkou) only when his zanpakutou is broken.
Ikkaku's bankai functions according to this principle. When he first activates bankai, his power is not at a level that would be considered typical for a bankai. He first has to strike his opponent and/or cut his opponent before his bankai starts to awaken. Even then, he has to wait for the dragon crest on his blades to fill completely with the colour red (like a power gauge) before he finally has access to his full bankai at proper bankai-level strength.
Hitsugaya has an immature bankai because his young age limits his power. As a result, to use its more powerful abilities he has to wait for the atmosphere to fill with a certain level of moisture first. Although he can circumvent this by using one of his zanpakutou's most basic abilities to control the weather, he doesn't like using it as it's also the hardest power to control and, because of his immature bankai, his lack of control can potentially be a problem.
Kyouraku's power is based on weaponising children's games. As a result, once activated, his zanpakutou sets the rules by which everyone - including Kyouraku - must fight. In other words, until his zanpakutou decides it's time for the rules to allow Kyouraku to use his more powerful abilities, he can't access them.
All captains and vice-captains have to be sealed to 1/5th of their power in the real world. If the situation is dire enough, they are allowed to break these seals.
Practically every soccer player (including goalkeepers) in the anime series Inazuma Eleven has this, which is called "Hissatsu" (Japanese for "Certain Kill").
All of the protagonists and eventually the antagonists too have Trans-Am. Around mid-way through the second season, the 00 Gundam aquires the 0-Raiser which makes it able to Trans-Am without malfunctioning as before... except that THIS Trans-Am is ridiculously powerful even when compared to the others; even the Gundam's designer is completely shocked at a RealRobotoutputting significantly more power than what it's theoretically capable of.
In the penultimate episode, Setsuna triggers a Trans-Am Burst which is truly this trope, filling several hundred cubic kilometers with enough GN particles to put everyone inside into a temporary Hive Mind - even ordinary, non-psychic humans. And if that's still not enough, The Movie gives us the Quantum System aboard the 00 Quan[T] which is even more powerful to the point the participants can share memories.
Mobile Fighter G Gundam has the "SHINING/BURNING FINGER!!". It's more of a finishing move, but in a closer sense, there's Domon's Super/Hyper modes, which (at first) can only be triggered by intense anger, then supreme calm. However, the manis boiling all the time, so it doesn't mean much. However, later, Domon mixes the Burning Finger with Master Asia's ultimate attack, so that has to count for something.
A Certain Magical Index: Accelerator's "Awakened" state, in which he develops black wings made of exotic matter and his powers skyrocket beyond the already ridiculously high level they start at. This only happens when Accelerator is under severe mental and/or emotional stress, so he's rarely thinking straight or even entirely coherently when in that form, making him all the more dangerous. When he finally manages to Awaken consciously, his wings are white and he gets a halo over his head. The exact ramifications of what this means have not yet been explored.
In Tiger & Bunny, the titular characters' Powered Armor enters the Good Luck Mode when they only have three seconds of their power remaining, which involves Wild Tiger's arm and Barnaby's leg virtually quadrupling in size, allowing for one final strike. subverted when, immediately following the first time Good Luck Mode is activated, it's revealed that it doesn't raise their power one bit. It was only designed to look awesome.
Thor'sGodly Essence Blast, often known simply as the 'Godblast' is an attack that takes a bit of charge-up time, and can even damage or destroy Mjolnir from overuse. However it lets him do things like drive away Galactus and break the armor of Celestials.
The Hulk's transformation could be seen as this, as it can only be triggered when Bruce Banner is in danger or under emotional stress (typically anger).
Final Fantasy VII: Advent Children had the characters using several of their limit breaks from the game. Many of them are not used as "limit breaks", though, after taking enough damage to fill an imaginary bar, but as just special attacks seemingly at will. Anyway, here's a list:
Barret seems to use a combination of his Heavy Shot and Mind Blow attacks.
Cid uses Boost Jump to smack Bahamut right in the brain. Ow.
Cloud uses Blade Beam against his foes in the Forgotten City, then uses Braver, Climhazzard against Bahamut Sin, Finishing Touch against Kadaj, and then finally an upgraded Omnislash against Sephiroth.
In Advent Children Complete, Cloud also uses the original Omnislash against Sephiroth. Sephiroth dodges Omnislash, which for those who don't know was the attack that, two years ago, finished off Sephiroth, banishing him from Cloud's mind. Sephiroth casually dodges it and then impales Cloud before he can come down with the final slash.
Yuffie can be said to have used Greased Lightning, but it's hard to tell.
Even Aerith, who's dead, gets in on the act by healing Cloud, and using Great Gospel to cure everyone of their Geostigma.
Although never said to be this, Thor's use of tornadoes and thunder seems to have one.
Live Action TV
Though nearly all seasons of Kamen Rider have Finishing Moves with awesome titles, Kamen Rider Fourze actually uses the term Limit Break. The trope isn't used, however - no requirement (other than it being the appropriate point in the episode) must be met before using finishers.
Exalted features 'Limit Breaks' as a part of the Great Curse placed upon the various Exalted at the conclusion of the Primordial War. Basically if a character has to act against their inclinations too often they eventually suffer a mental break which makes them even more powerful than they were but sends them out of control, whether on a psychotic rampage, cowering in a cellar or unleashing a hitherto unsuspected sadistic streak it typically ends badly for all concerned.
The only Celestial Exalts not to suffer this are the Abyssals who have it even worse...
This means that tabletop role players who are unfamiliar with the computer RPG meaning will tend to think of a Limit Break as the Exalted version, and thus be confused...
It's not entirely a bad thing; it does provide a Willpower refill. Of course, this has to be balanced against turning into a sadistic bastard, entering an Unstoppable Rage, entering into a temporary Heroic BSOD, or giving away all your cool magical equipment...
Burn Legend, in Shards of the Exalted Dream, has Overdrives, which charge up when you hit your enemies. Overdrive techniques tend to have enormous clash pools, deal massive damage (sometimes to multiple targets), and automatically force the enemy to lose a health stock and take a roll to remain consciousnote except a few oddities like Demon Emperor Shintai, which instead provide you with a significant stat boost or other long-lasting benefit. Of course, if your opponent knows what your Overdrive is, you might be advised to assume they'll try and counter it, so then you use a technique that beats their most likely countermeasure. And then there are the few techniques that force stagger checks or even automatic stagger on an opponent, which will give you a chance to ream them while they can't counter you.
The tabletop wargame Warmachine from Privateer Press features similar abilities amongst the warcasters called feats. Feats can only be used once per game, but when used properly can turn almost certain defeat into victory.
Also from Privateer Press, Monsterpocalypse has Hyper Mode. Every monster can hyper-up by spending power dice, entering Hyper Mode (depending on the figure, Ultra, Mega, or Quantum). Both the Alpha and Hyper forms need to be defeated, so this crosses over with Turns Red.
An optional rule for the free RPG ZODIAC introduces Limit Breaks in a similar style of those of Final Fantasy VII. It only makes sense, as the system itself was designed to give the feel of a Final Fantasy game.
There is a particular rule in Fading Suns, which allows a very unsettled character to snap and go for Unstoppable Rage or other kinds of fanatical fun. If the appropriate test is passed, the character receives bonuses to other tests until the matter in question is resolved. It may require some tact from the GM to execute it properly.
Masters in Malifaux can manifest Avatar forms, giving them access to new and improved abilities. To manifest, they have to meet a set of requirements specific to each Master, usually based on using that Master's unique abilities successfully.
BattleTech features the Triple Strength Myomer equipment, which upgrades the battlemech's artificial muscles to work at triple strength and speed. However, they only receive the strength and speed bonus as the mech is nearing critical heat levels. Once at optimal heat from combat or just dumbfiring its weapons (at which point, the targeting computer begins to fail), a TSM equipped mech will be absurdly fast and possess the ability to nearly instantly kick the legs off enemy battlemechs or literally curb-stomp fallen mechs by crushing the cockpit. Pilots of TSM mechs need to be careful to maintain their heat level without increasing it too far, or they run the risk of spontaneous death by causing any ammunition in their mech to explode, or have the fusion reactor burst inside the mech's chest.
In Cardfight!! Vanguard, there is a skill called, word for word, Limit Break, which activates when the player has 4 or more damage (the player loses when he/she has 6 damage). Limit Break skills generally have strong effects such as boosting power, destroying cards on the field, adding extra cards to your hand, etc., to help the player turn the table.
Taken Up to Eleven when Ultimate Break is introduced later. These skills only activate when a player has 5 damage.
There's also the Damage Trigger Check. As you take damage, your Vanguard may grow stronger (so you don't need to defend as much that turn), and in addition, you may draw a card, or even heal some damage.
Megablast abilities require you to counterblast five cards' worth of damage and remove eight cards from their soul, but allow you to pull game-winning effects like standing all of your units for another two attacks, providing a significant permanent boost to the mega-blasting vanguard, or (most commonly) destroying all your opponent's rearguard units.
Yu-Gi-Oh!: Number C39: UtopiaRay can only activate its effect if your Life Points are 1000 or less (you start with 8000).
Planeswalker cards in Magic: The Gathering. Each planeswalker has a powerful "ultimate" ability that can only be used after building up its loyalty over several turns and is often designed to win the game shortly after it's used. Since a planeswalker's loyalty also functions as its health, damaging a planeswalker is actually the best way to stop this from happening.
Krillin of Dragon Ball Z Abridged unleashes his in Episode 7 to kill three Saibamen... and is immediately upstaged by Piccolo. As consolation, Vegeta and Nappa conclude that "Earth's Raditz" is at least not quite as pathetic as their Raditz.
Found all over the place in Pirate Baby's Cabana Battle Street Fight 2006, where the two characters will call out something else to bulldoze through the enemy, including The A-Team and Walter Sobchak.