The status effect Daze. Daze critically slows the enemy's movement speed and lowers their ability to aim by a huge amount. It also, inexplicably, cuts projectile velocity, so their bullets travel slower. Lilith has a skill that can give a 25% chance to inflict Daze on each bullet she hits with. Her main weapon is a submachine gun. Mordecai has a pet bird that can inflict Daze 100% of the time. The bird is computer controlled, so it never misses, and can attack up to nine different enemies in a row, along with inflicting other status effects. With the right class mod, the cooldown can even be reduced to a mere two seconds. This game also has PvP combat. So yeah.
In solo play, nothing comes close to a Hellfire SMG. Most of these have high rates of fire and decent firepower. All Hellfires come with a 100% chance to ignite the enemy. Fire is by far the most damaging status effect, and the fire from a Hellfire can stack. A quick burst of sustained fire against a group of enemies can leave them dead in seconds with little ammo consumed. Hellfires are extremely effective when playing as either Roland or Lilith, who can both regenerate ammunition with the right Class Mod.
It may not be as ridiculous as the Hellfire, but the Defiler revolver is definitely the closest thing to a corrosive equivalent. It has a 100% chance to corrode enemies, and on top of that, corroding enemies take more damage from all sources. Any character can use it effectively, but Mordecai deserves a special mention, since he can boost its already preposterous damage output with an Assassin Class Mod (not to be confused with Mordecai's Borderlands 2 equivalent Zer0, whose class name is Assassin), which increases his corrosive damage by at most 60%, and all of his pistol and critical hit-buffing skills, and you can wreck badass Crimson Lance within mere seconds.
It gets worse; Lilith herself is something of a Game Breaker. Combine her 25% daze ability with a Hellfire, crank up the damage and fire rate, then give her maxed out Phasewalk time, regenerating health during Phasewalk, and get the perk that cuts six seconds off your cooldown with each kill and reduces damage taken immediately after coming out of Phasewalk. The result? Even if you are reduced to almost no health, just hit Phasewalk, fully regen all your health (whilst moving at super speed, while both invisible and invincible), then when you reappear, gun down at least two enemies (who are going to be immediately dazed). By the time you finish killing the second enemy you can Phasewalk again and you won't have even taken any damage yet. It pretty much makes Lilith unkillable enough that she can solo Crawmerax with ease.
Pearl Shotguns if you like to use boomsticks. A sniper-esque shotgun in essence.
The Dove. Despite not consuming ammo and no need to reload, it seems fairly weaksauce compared to other pistols. However, with the right combination of skills and perks—most notably Mordecai's Gunslinger skill—the thing becomes a freaking machine pistol that never needs reloading, meaning you'll never need another gun if you play your cards right. To put this in perspective, I've seen players beat the Rakk Hive with nothing but the Dove and a few health power-ups.
Brick's kill skills Revenge and Master Blaster are by far the biggest DPS-boosting skills in the game, granting him ridiculous damage and fire rate buffs, respectively. Throw in his explosive damage buffs and the Atlas Ogre combat rifle and you've got arguably the highest-damaging combination in the game.
Mordecai's skill Carrion Call allows him to reduce his Action Skill cooldown simply by shooting an enemy with a sniper rifle. The Skullmasher, the legendary Jakobs sniper rifle, shoots 6 bullets at once. Combine those two and you'll never have to worry about cooldown again.