The Shining Laser is a possibly intentional example. It can down bosses faster than Sonic the Hedgehog. It sort of balances out, though, because it's not available until late in the game and costs a LOT to upgrade its stats. Lampshaded when Roll admits the power of the weapon is so great it almost frightens her.
If you beat the game once, you unlock Hard Mode, where everything has more health, takes less damage, and deals more damage. Beat the game on Hard Mode and you unlock Easy Mode, which is for all intents and purposes identical to Normal Mode, but you start with a part that you can equip that maximizes every attribute on your Mega Buster (an impossible feat in any other mode) which means extremely high attack power, extremely long range, you never have to stop firing your Buster, and your Buster shoots extremely fast. Combine that with the never-ending circle strafe strategy mentioned below makes short work of every boss in the game, including the super-resilient final boss. Additionally, easy mode cut a bosses normal mode HP in half, and it takes twice as long to bust your shield.
The Active Buster is pretty good as well, being a homing missile launcher. Although it's a just a touch weaker than Shining Laser in attack strength, once fully upgraded the other stats are at the absolute limit, turning it into a long range missile machine gun.
Balanced in the fact that the really breaking part of the Active Buster is the final Energy upgrade, which gives you infinite ammo. With a weapon that has nearly infinite range and is only out-damaged by two other weapons in the game. The final Energy upgrade alone costs more than the total price of any single special weapon in the game, more than 100,000 Zenny (in-game currency) more than the Shining Laser total, the most powerful weapon in the game.
In 2 the Homing Missile replaces the Active Buster, is gotten as early as the Ground Crawler and unlike the ground crawler which can't hit floating enemies this one can, the only downside is it's super expensive, almost as expensive as the Shining Laser, the thing that makes it so good? Well for one the explosion knocks any smaller enemies over, those reaper thieves? Immune to the Buster Gun and Ground Crawler? The Homing missile takes them out in three shots. Second it fires FAST! Very fast, so fast in fact that you might end up accidentally having to wait for it to load back up before firing it again. Thirdly it's insanely effective against the Final Boss, who borders on SNK Boss at times.
The Drill Arm in Mega Man Legends 2. No, seriously. If you max out its attack power (Which doesn't cost very much) the bosses of the first two major dungeons will die as soon as the drill touches them, and there are plenty of opportunities to get close enough to do so.
The Ground Crawler, again in Legends 2. It's inexpensive to upgrade and MURDERS ground enemies. It even nails air enemies that dare get close enough.
Circle strafing, in general, is THE go-to strategy for this series if you don't have the above mentioned weapons.
A non-combat Game Breaker is the Vacuum Arm. This will suck in refractor shards for you; since they don't last very long, they're normally a pain to pick up, but with this Arm you'll never miss a one. It gets infinite energy with a single upgrade; once fully upgraded, it can suck in a whole room's worth of refractors near-instantly. Get in the habit of using this thing and you'll be very rich very fast — which makes the whole rest of the game easier.
Another non-combat one is the giant golden bird-reaverbot in the Pokte Caverns on Manda Island. It drops a fairly large amount of zenny, can be killed without too much difficulty, and unlike any other enemy in the game, it respawns every time you exit and re-enter the room. It is hands down the best method for money grinding, and it can be found only about a quarter of the way into the game!