In the earlier games, X can find some well-hidden Street Fighter II-inspired Easter Eggs that let him perform a one-hit kill (or near one-hit kill) attack, thus making the game a whole lot easier after finding them. This is balanced out by the fact that they can only be found in the final boss stages and can only be used at full health, in addition to requiring Street Fighter-like input commands that make them difficult to use in battle. Examples of this are the Hadoken in X1 (which had an added problem of being hard to aim against Sigma) and the Shoryuken in X2.
X3 has the Gold Armor, which is a true game breaker. There are four booster chips in the game: armor booster that gives a 75% damage reduction shield when hit, a special weapon that allows you to spam Charge Shots, the power to dash twice before dropping to the ground, or a healing factor that would not only restore your health but fill sub-tanks. If you don't collect any of those but do find every other item in the game, you can get the secret Hyper Chip early in the fortress, which gives you all four abilities. In other words, you get nearly four times your normal health in addition to a host of abilities that make your character quite unstoppable.
X1's Storm Tornado. Storm Eagle wasn't exactly easy to defeat if you chose him first, but it was doable. And the weapon he gives you can kill pretty much every non-boss in one shot, and do a lot of damage to bosses.
If you got the Dash before that, he was easy. His most dangerous attack is the one that doesn't damage. but instead pushes you back off of the edge of the platform. Spamming dash can counter that. Plus it lets you fairly easily dodge the rest of his attacks.
X3 had X wielding Zero's beam saber, which was more versatile as it was an upgrade to the charge shot and didn't need a health requirement to fire. With a proper hit, it kills any non-boss enemy instantly and had piercing on top of that (a novelty, but occasionally useful). Any boss enemy would, with a proper hit, be reduced to 20% of their max HP, including the final boss. Combined with the double X-Buster shot that had to be fired prior to the beam saber swing, the result could kill anything with one ten second charge, which is trivially easy to manage.
X4-X6 gave X the Ultimate Armor, with infinite Nova Strike, while X8 had an upgraded version of this. Unlike X and X2, none of these required you to have full health. None of them were one-hit finishers either, although several were two-hitters.
Ultimate Armor allowed, as previously indicated, infinite Nova Strikes, which in other armors is an attack that affected either the entire screen weakly or one particular area strongly, and then required a lengthy recharge time. The Ultimate Armor allowed Nova Strikes to be chained indefinitely, and they differed greatly as well, turning X into an invincible jet that causes collision damage. In addition to unleashing a devastating attack that can take out any boss in about ten seconds, the Ultimate Armor also allowed X to traverse difficult platforming sections by granting the ability of unimpeded flight.
Xtreme 2, a game for the Gameboy Color, had a part system like the one in X5. X could equip up to four upgrade parts as long as he didn't have all his armor parts, if he did only two were possible. So as long as your were willing to give up the upgrade for the Street Fighter moves, much weaker than the console versions, you could skip the helmet, which was identical to the X1 version. The best part loadout was Buster +1, Buster +2, Ultimate Buster, and Speed Shot, letting you forget the special weapons and just blast away with a high speed barrage of double-strength charge shots from the X buster. Or you could skip speed shot for the Hyper Dash, which makes you invincible when dashing, and add some defense to your still hideously over-powered offense.
There's also the Plasma Buster Upgrade that debuts in this game. Fires a large and damaging plasma shot that penetrates everything, and leaves behind a ball of energy that does continuous damage to rip up Mooks to shreds. Later games reserved this for the Fourth and Ultimate Armor only.
X5 had the Falcon Armor, which you could get pretty early on if you knew where to look. As the name suggests, this armor gave X flight. Not brief flight, either; flight time was very generous and could be instantly reset simply by landing and taking off again (even a wall cling would suffice), in addition to flight speed being pretty good. Furthermore, the flight also comes with a Battle Aura that can cause damage or outright kill weaker enemies (and some bullets), though you couldn't just plow through everything. It didn't even have any real drawbacks, either. In exchange for a trivial reduction in charge shot size, X gets a piercing attack that is extremely useful and a screen-cleaning Giga Attack. This was so powerful that it was brutally nerfed in X6, completely eliminating the flight ability, reduced the Buster power, and reduced the Giga Attack damage so much that it was weaker than its Charge Shot. Next to the Ultimate Armor, this is probably the biggest Game Breaker in the X series and the biggest nerf that X series ever have during game transition.
The Gaea Armor, while it slows X's dashing speed, has short-ranged shots, prevents him from using any parts and, special weapons, and lacks air-dashing, the Gaea Armor gives him a powerful X-Buster that not only has a destroy some enemy shots, but has a ridiculous charge speed. He can literally spam charge shots like no tomorrow, and these charge shots ignore bosses' Mercy Invincibility frames, allowing him to create a Cycle of Hurting on bosses.
X6 had, like some of its peers, a parts system. It also had an armor whose charged attack is a sword slash. Remember this. Some of the parts included one which would make all your attacks fully charged, typically draining your shot speed a bit. Another part would cause a charged shot to 'stick', doing some extra damage as it passed by an enemy. There may have been a third involved. Now, we have an armor on that has a charged sword attack, with no uncharged attacks available thanks to a part, and another part that makes charged shots stick... but the sword continues to hit the enemy. What this translates into is you basically break the game against anything without immunity frames that you can get close enough to to hit.
Rather unfortunately, though, everything you might want to use this on (bosses) all have immunity frames, forcing you to have to wait 5 seconds every time you hit, since the game lags every time you do this. Though it works wonders against the final boss. But so does the Ultimate Armor.
Then again, Zero can essentially ignore boss immunity frames, since they don't trigger on the Z-saber until the third swing hits (with one exception in X6). And dashing cancels a slash combo. And switching directions stops a dash. It's no wonder why the tool-assists of X5 and X6 use X only when Zero is not available.
A nice part load out for (normal) Zero in X6 is buster plus, saber plus, double barrier, shock buffer, and life recover. You get enhanced attack power, doubled defense, double the time you're invulnerable after getting hit, and basically a third sub-tank.
The Guard Shell, possibly the most broken weapon in X series for Zero, and a candidate for the most broken things ever existed in X series, on par with Ultimate Armor and Falcon Armor. Basicaly, the shield normally only reflects attack as its name and the game text would imply. However for Zero it has two effect. One is the written effect, and the second effect is multiplying the hit number of close range attack such as the Buster, and the Saber slash combo, and it ignores boss immunity frames. Essentialy, you can beat most bosses in the game at 2 second using this move.
X7, while has Infinity+1 Sword vibes, X himself count. Well everything is normal for him like the other game, however when he have a Strong damage output from charged buster that does damage as high or higher than super effective weapon on boss and said charge shot homes in AND as big as half of the screen, its definitely crazy.
Mega Man X: Command Mission had Bait/Stealth Form, which allowed Axl to always be the target of any targeted attack and not take damage. Not a perfect lock, as attacks that hit the whole party would still be able to hit your other characters, but good enough to make many boss battles a lot easier.
And then there's X's Ultimate Armor and Zero's Absolute Zero armors, which increase your attack power to the point that 25K damage can be done with each character. Boss battles will NOT last long enough for the power-ups to eventually wane like they do after a few turns if you use Build Hypers to increase the time the power-ups last. Add SFM Fragment Alpha and you can get a Limit Break out EVERY TURN.
It should be noted, however, that the Ultimate Armor and Absolute Zero are more infinity plus one forms rather than actual game breakers. Both require you to defeat a ridiculously hard Bonus Boss for each one (The Mole Brothers for Absolute Zero, Rafflesia for Ultimate Armor X). The aforementioned SFM Fragment Alpha can only be obtained using Marino's Limit Break on the Final Boss of the game.
X8 has the Σ Blade, the sword Sigma uses in the final battle. Zero becomes a literal walking murder machine with it.
On the subject of the heroes' Infinity+1 Armors...
X's Ultimate Armor in this game has the limited Nova Strike, however it will damage them severely (about 97% of their HP gone in a single hit) and charges REALLY fast. It also takes X4's helmet upgrade to the extreme by allowing him to have infinite special weapon energy for both normal AND charged attacks.
Zero's Black Armor fixes his short dashing distance and turns him into a Glass Cannon. Combining this with the aforementioned Σ Blade lets Zero turn enemies into mincemeat.
And finally Axl's White Armor gives him indefinite hovering while firing his weapons, faster dashes, and unlimited transformation time. Feel free to speedrun your way to an AAA/S rank with ease.
Mixing X's Hermes Helmet with the Icarus Buster allows X to spam fully-charged shots (not the Wave Motion Gun although that can also be spammed) like crazy, similar to X5's Gaea Armor only without the crippled dashing speed and retaining the use of his special weapons. These shots ignores their invincibility frames (except when they're using their Desperation Attack) instead of triggering it since it's no longer the guard-breaking attack for bosses.
In Maverick Hunter X, you get to play as Vile. He's got a few breakers up his sleeve, too. One example is the Stubborn Crawler which absolutely MURDERS anything on the ground and on a wall faster than you can blink. In addition, not one, but TWO bosses are weak to it. Then there's the Parasite Sword, which can hit anywhere on the screen if you're positioned properly. It cannot be destroyed, and it's pretty powerful, too. The kicker? There's no limit to how many times you can use ANY of his weapons.
From the vulcan weapons, there is the Distance Needler. Acquired by beating Chill Penguin, this weapon has a slower firing rate than other vulcan weapons. However, it does have a longer range, can pass through just about any enemy (even shielded ones), and deals a pretty good amount of damage per shot. Plus, this weapon can be equipped with both of the ones mentioned above, thereby validating Vile's character as a one-Reploid murder machine.
And from the Missiles, we have the Popcorn Demon, which fires one missile that splits into three. Far and away one of the most easily spammable weapons in the game; it takes only a couple of seconds to fill half the goddamned screen with missiles and cause the PSP to lag. You can then use the resulting slowdown to spot and dodge incoming attacks.
The game also tweaked some of X's weapons. The arm upgrade you get from Zero is stronger than the normal version, making the buster a good alternative to Rolling Shield. Rolling Shield got the most out of it though, as you can switch weapons while the charged barrier is up, so you can have the free hit and fire anything (including the fireball).
If you're holding a charge using the primary fire button, and you execute the fireball using the X-Buster button, X will fire a Hadoken without dropping the charge on his main weapon. You can also map the X-Buster button to one of the PSP's shoulder buttons to make it easier to pull this off.