FPS isn’t usually my thing but I love sniper rifles. Like the ones in Goldeneye and Call of Duty.
The (I think it was a Barrett Light 50) sniper rifle in Far Cry. Any sniper rifle, really, but that one especially.
Silenced PPK in Goldeneye. The first time EVER that you kept going back to your start-off weapon. The right tool for the right job.
This was actually what I came in to say! :: pleased ::
I also love shotguns, both in games and in real life, so I like most of them. But the first time I put my hands on the auto-shotgun in SOF II…
…sweet.
Absolute favorite was the SMG with grenade launcher from Halflife. Once I picked that one up in multiplayer, I had no need for any other weapon.
A close second would be the Barrett .50 caliber from Rainbow Six: Ravenshield. The first time I hit a bad guy with it he flipped head over heels, and I fell in love. It was always a hoot packing one of them along on a cooperative mission requiring secrecy, where we’d spend 15 minutes sneaking up on the targets, the only sound our own footsteps, and then scaring the crap out of my friends with the horrifically loud report, despite the silencer.
My vote for most fun weapon - the Land Shark gun from Armed & Dangerous. Once fired, it would roam around underground killing any enemy it found. Often an enemy would hear a noise, say “what’s that?” and be met with the shark popping up on it Jaws-style. Screenshots from the X-box version (a few rows down for the shark).
The Laser Rapier in System Shock was very cool as well.
I totally agree! The best part was that it seemed to have some sort of mod that made you able to hear conversations from hundreds of yards away. The second best sniper rifle, IMHO, is the rifles they use for the Delta Force series…you can peg someone from a mile with those!
RCP90 in Goldeneye.
Alien raygun from Southpark that made the victim sing and dance.
Rocket launcher from UT with multi rockets, grenade launcher secondary, and homing rocket.
Farsight from Perfect Dark (sniping with heat vision through walls).
Gravity Gun from HL2.
GI (Gastral Intestinal) Disruptor from Science and Industry.
BFG-9000 and combat shotgun from Doom.
Energy Sword in Halo 2.
the shotgun, doesnt matter what game, its the ideal close range weapon and with a sawed off you can gank multiple opponents at once.
the mortar from Tribes 1, god damn that green smoke was scary when you saw it landing near you.
I always liked camera missles, which I first saw in PO’d. Zipping around until you rammed something and blew up was fun, even when it was yourself.
Counter-Strike’s AWP, just for the controversy.
It’s hard to think of a single weapon from any of the other games I played that was so versatile. It had two drawbacks: splash damage and the inability to have both multi-fire and single-fire at the same time (of course, if you DID have this option if you didn’t mind only having semi-auto fire to shoot one rocket at a time).
I like miniguns too. The one in UT was the best I ever used too, although admittedly I haven’t had a lot of experience with FPS since around 1997 or thereabouts.
The shotgun is also very practical in just about every game that has one, but it’s not very amusing or spectacular. One complaint I have about UT is that the Flak Cannon, the next best thing to a shotgun, has a very limited range. They did fix this somewhat by UT 2k4.
As for amusing weapons in FPS, where to begin…
In UT 2k4 I love how you can shoot someone’s head off with the lightning gun leaving behind the flaming stump of their neck. Likewise with the shock rifle in insta-gib. It’s funny how the lower part of the corpse just flops over like a dead fish.
I got a kick of the way the charred skeletons crumbled to the ground after getting hit by the firewall in ROTT. That xylophone effect of the bones clattering was the icing on the cake. The hand of god in that game was pretty neat too.
Maybe it was because I was 13 when I first played it, but Doom in general was always hilarious to me. The sound of the rocket launcher and plasma rifle always makes me smile, and it was cool when you would blow someone to pieces (“reduction” as my friends and I called it).
UT had the chaos mods too, with the proxy mines and the gravity vortex. The latter was especially cool.
I could go on, but those in particular stand out in my mind.
I always loved the Mech-Warrior series. Having a whole Mech as a weapon you get to climb into and drive around! I guess that’s not really in the spirit of the OP, so I’ll pick the Gauss rifle on my Mech. Cool sound and visual effect, and possible one shot kills. Limited ammo forced you to learn to use it.
The flak cannon from UT 99 was my all-time fave. I loved the masses of enemy-shredding shrapnel you could fling at a hallway full of foes. You could ricochet it around corners, and as an added bonus, its alt-fire was a ridiculously effective flak grenade. Bonus points for coolness because when you were on the receiving end of the grenade, and your enemy achieved a direct hit with it, the last thing you saw was a brightly glowing smiley-face inscribed on the surface of the grenade.
Also awesome was the Redeemer. A mini-nuke that could level half the enemies on the map, and was camera-guidable? More, please! Hell, just the sound of that thing being launched was enough to send EVERYONE scurrying for a hiding place.
I also have to give mega fun points to the stake gun from Painkiller, though. I loved nailing enemies to the wall with it. Only bad thing about the game was that the enemies disappeared after a while. I always wanted to wade through the corpses of my fallen foes after a battle.
The bowie knife from Serious Sam. Hefty damage and it had this sort of ponderous feel to it, like the blade was made from solid depleted uranium. Felt like it had serious mass to it.
Other than that…Garrett’s blackjack from thief. Dang, that baby was handy. 
Another vote for the Flak Cannon, any incarnation. I don’t know if the other weapons have equivalents, but I’ve gotten “Flak Monkey” so many times it’s ridiculous.
The Temporal Uplink in Timesplitters: Future Perfect is surprisingly useful, too. It works like a remote grabber/thrower. Enemies in Future Perfect will often take cover behind a crate. It’s pretty funny to grab the crate with the Uplink and proceed to pwn them with it.
Another vote for the HL2 gravity gun. Nothing is cooler than killing a someone in mulitplayer with a well flung toilet. 
And when I got the super version at the end of the game, I cracked manically and yelled out “I am become death!” 
The Concussion Rifle from the original Star Wars: Dark Forces game.
It was a lovely thing. Long range, accurate. When fired, there was a lovely moment of hesitating after it went off, as if the universe were holding its breath in anticipation the ensuing carnage.
Then, that lovely blue bolt hit. An euption of lucent energy filled the area. And all the imperial saround it were blown into a galaxy far, far away. That was a not a gun, friends. It was a symphony of murder.
I don’t play many FPS’s, as I have a problem with motion sickness, but since I’m often on the receiving end of my brother’s massacres in Goldeneye and Perfect Dark, here’s the weapons that really stand out in my mind:
*The unarmed downward chop, Goldeneye. Especially hilarious in “Golden Gun” mode.
*Grenade Launchers, both games. I always end up with more suicides than kills, but they’re still muchly fun.
*The RPG 90, both games. Sick, sick weapon with lots of firepower.
*Tranquilizer Darts, Perfect Dark. The first time I saw the effect on a person, I couldn’t stop laughing. “OMG, I’m stooooooned!”
*That weird funky experimental weapon in Perfect Dark that can shoot through walls. Massively unfair weapon - all you hear is the “ZOW!” and you die.
I will second the pistol from Halo: Combat Evolved. So powerful, so accurate.