Game Breaker/Mass Effect

Mass Effect

 * The humble Pistol was the weapon of choice for most people, even beyond several of the weapons found later in the game. It had the best accuracy, damage, rate of fire and was available from the beginning of the game. With a little tweaking, you could turn it into a good long range killing machine (without bothering to use the Sniper Rifle). The pistol's Marksman ability, at maximum, will also out-shoot Assault Rifles easily - more rounds, more damage, less heat and more accuracy. With the Infiltrator class, specializing in Commando, as well as a Medical Exoskeleton, it can speed up the recharge on Marksman to the point where you can have the skill enabled permanently.
 * Now combine Pistol's Marksman with the Immunity ability. You can basically stand still right in front of a pack of six enemies who all have guns blazing on you and methodically take them all down one by one before Immunity wears out. This will work on any game difficulty! The only problem with this is the presence of an enemy biotic who can knock you down on the floor repeatedly, but there is only two or three of those specific instances in the whole game.
 * An Adept's skills, when set up properly, lasted longer than it took for them to recharge. On top of that, they have the ability to damage anything in a Stasis field, which can't fight back. This ability works on the final boss.
 * Adrenaline Rush. Unlike the later games, each power in ME1 had its own cooldown, independent of all the others. What Adrenaline Rush does is reset the cooldowns of all your powers so you can use them again instantly. In the hands of a Vanguard, this essentially amounts to dual-casting Lift, Throw, and Barrier, with a side of Marksman/Carnage for good measure. And by the time all those run out, you'll probably be ready for another Adrenaline Rush. Oh, and since you've got a bio-amp anyway, Vanguards are ideal for using a biotic bonus power like Singularity for even more chaos. And in case you're worried that tech powers were left out of the fun, Garrus also packs Adrenaline Rush for all your rapid-fire-Overload/Sabotage needs. Enjoy.
 * Soldiers and Infiltrators both could get Master Immunity and a specialization to reduce its recharge time to be identical to its duration. This ability made the player virtually invincible and could be reused as soon as it wore off. It completely negated the need for cover, which is supposed to be a major defensive component. It also negated the benefits of taking defensive bonus talents, which were pretty logical choices for a Soldier if you didn't realize how effective Master Immunity was.
 * The Spectre Master weapons, gained by amassing a million credits and buying them from the C-Sec/Normandy requisitions officer (and can be done very early on, if you save enough). Every other gun pales in comparison.
 * Though in the Insanity difficulty, they are merely what you need to survive.
 * Take Tali. Max out Quarian Machinist, Electronics, and her gun skills. Give her the quarian armor from 'Bring Down the Sky' and the best shotgun you find. In terms of survivability, she'll outclass Wrex.

Mass Effect 2

 * The Mattock Assault Rifle for the soldier. It deals ungodly damage in Adrenaline Rush, is extremely accurate, and is available from the start of the game.
 * The M-29 Incisor Sniper Rifle is a DLC weapon that does decent damage when Shepard equips it, and is available from the beginning of the game. Give it to your allies, however, and you can walk through most of the game without firing a shot, especially on Insanity difficulty (and right from the beginning of the game). As this video shows, Zaeed and Garrus will mow down most enemies in three or four shots, while the player can stay behind and play "spectator" as the AI kills everything in the way with massive damage. According to the game coding, squadmates do reduced damage on higher difficulties with most weapons except those obtained through DLC, making the M-29 king of the hill.
 * Like the aforementioned M-29, Kasumi's M-12 Locust can also be obtained incredibly early in the game, and has the highest base damage and damage multiplier of all SMG's in-game, making it ridiculously good for most enemy encounters. In terms of damage-per-second, the M-12 also beats most midgame weapon pickups, and doesn't require Assault Rifle training for Engineers, Adepts or Sentinels. The only downside is a slightly lower clip capacity.
 * Then there's the M-98 Widow Anti-Materiel Rifle, available to Soldiers and Infiltrators on the Collector Ship. With the proper powers activated (the Soldier's Adrenaline Rush or Infiltrator's Tactical Cloak plus appropriate ammo, with Warp Ammo being the best choice for all but shields) and the right armor/weapon mods, it can one-hit kill most enemies in the game with a headshot, even on Hardcore or Insanity difficulties, even if they're protected. The only downside is the small magazine (only holds one shot) and relatively slow reload.

Mass Effect 3

 * Vanguards have become field-wipers thanks to their new ability, Nova. Nova is normally a Death or Glory Attack because it drains your shields to cause a huge biotic explosion. However, the vanguard staple Biotic Charge regenerates shields whenever it's used correctly. Should a vanguard equip nothing but a light pistol or SMG, the cooldown between the two would be short enough that a fast player could jump around blasting any enemy in range over and over again until all that's left is a pasty smear on the wall. The only downside is that it can lead to a player's death if they get too far from their allies (or teammates in multiplayer).
 * Now that Overload works against both regular shields and biotic barriers, it's surpassed Warp as the go-to anti-defense power. In addition, it's later evolutions can make it jump from target to target chain-lightning style, as well as impart a neural shock effect. Put all these together, and you've got multi-target, anti-shields, anti-barrier, and stun, all in one power.
 * Likewise, the Energy Drain power has also gotten a similar boost. It can't chain like Overload, but simply making it usable against barriers means that no matter whether you're fighting husks, Cerberus, or, there's at least one enemy type available to drain from.
 * This is particularly useful for Infiltrators, since they don't get Overload by default, and the main drawback of Tactical Cloak is that your shields do not recharge while it's active. Energy Drain solves both problems, which is why Salarian Infiltrators (who have Energy Drain) are so prominent in multiplayer.
 * The N7 weapons included in the Collector's Edition are all near or at the top of their class, are available from the start of the game, and (with a mod or two) become devastating:
 * The N7 Crusader Shotgun. It fires a single, accurate, solid slug rather than shot. This essentially makes it an unscoped sniper rifle, with comparable stopping power to the single shot sniper rifles...except it's semi-auto.
 * The N7 Eagle. It's got the accuracy and power of a pistol, and the fire rate of a SMG. Put a scope on it, and you have a full auto Sniper Pistol. Like the Particle Rifle, you can probably take nothing but the Eagle and do just fine.
 * The N7 Valiant sniper rifle. Like the prohibitively expensive Black Widow, it combines a three-shot clip with good stopping power. Unlike the Black Widow, its recoil and reload time are practically nonexistent, making room-clearing a breeze, and it's light enough to keep power recharge high, or maxed out with upgrades.
 * The Particle Rifle (from the "From Ashes" DLC) runs on the same "cooldown" system from the original game, but also uses a beam that gets stronger as the trigger is held down. Not only can the weapon be acquired extremely early (by doing right after Mars), but it can also be augmented like the other weapons with mods. A Particle Rifle with a magazine upgrade and extended barrel will have much more ammo than normal, and will chew through enemy defenses easily, even on Insanity difficulty. Even better, if a Soldier class runs the beam's ammo down to 0 and uses Adrenaline Rush, the weapon's reloading animation (which often takes several seconds) is skipped and the ammo will refill again, saving precious seconds in combat.
 * On anything less than Insanity, where the AI becomes smart enough to work around it, Tactical Cloak is this. While the Infiltrator's signature weapon is the sniper rifle, using Tactical Cloak with just about any shotgun, the Carnifex, or the Paladin means you can run around a map free from enemy fire, walk right behind them, shoot them in the back of the head for massive damage, hide behind cover for what might be, depending on your level, 3 seconds and then you can do it all over again.
 * This game's version of Stasis has the most potential for game breaking yet. Unlike the first two games, enemies under the effects of Stasis can take damage (though too much damage will break the stasis effect). It also acts as a source power for biotic explosions (which means you can follow up with Warp or Throw for massive damage), it ignores shields and barriers (so Phantoms among others are not immune to it), and a Rank 6 evolution lets it create a bubble that will stun any unarmored enemy that walks into it, essentially making it a multi-target trap like Singularity.