Are TPS games allowed? If so, gonna chime in for everyone's favorite ME3 sniper rifle, the Black Widow. Three rounds a mag of cover-piercing headshot delight. Honorable mention goes to the ME2 Revenant. Long may he be mourned.
If not, the Spas-12 from Trepang2. Yes, its pump action only, but if you dual wield you literally throw it up ahead of you so you can grab it by the foregrip and pump it before tossing it back into your hand, ready to fire. And you can either alternate fire to maintain a steady stream of death or double-click if you want something dead. The best part is that it somehow works even if you're running and jumping around like an Unreal Tournament player. Someone else already mentioned the Quake 4 weapons, and I'll say my fav there was the railgun.
For something unmentioned, the frag grenade from Starship Troopers: Marauder, an old and not entirely terrible FPS. What makes it special is that when you cook it a cute little pixel-tone smiley face appears on the grenade and counts down the detonation timer in a cheery tone for you. And since New Vegas is technically an FPS (or should be unless you're a third person fag), the
Holy Hand Grenades of Searchlight. Damn shame they're Wild Wasteland only.
So much fun, especially if you snag a mod that gives it extra long pinning distances on a kill. You'll send guys flying across the room to dangle by their wrist and ragdoll for all eternity.