I have to add proximity mine from Goldeneye 64 and laptop gun from Perfect Dark. So fun to use.

Golden gun from Goldeneye is kind of imbalanced, but it sure created some tense multiplayer moments.

gimme a Gatling and I'm happy, like the Raven in SHadow Worrior 2

Sword of the Dragonclaw from Dark Messiah of Might & Magic. With it and a lightning shield I'm a lawnmower going thru dry grass.

https://www.youtube.com/watch?v=HobiJxeOKg4

https://www.youtube.com/watch?v=PQc7x8eY5Aw

Last Prism from Terraria.

Saints Row 4 has some of the best weapons of all games. For example the Rectifier Probe and the Inflato-Ray.

If there's a boomstick, you can bet it's my weapon of choice.

I see that and raise you the Disruptor Rifle(the one that has sniper scope) in Jedi Outcast......one shot can kill most enemies(non boss) with one scoped hit.

There are several, but first that came to mind is YCS/186 from New Vegas. Talk about a powerful gun...

Also Aerondight (as seen in Blood and Wine) and Blood sword (The Witcher 2 / Roche's path).

too many games, too many weapons to remember...
After a little research (i'm getting old, i don't remember every single weapon i use in all games i played):

Baldur's Gate - Long sword +1 Flame Tongue (love the flame effect)
Baldur's Gate 2 - Celestial Fury and Hindo Doom (as Cespy said: Hindo's Doom! Can you say it? Hindo's DOOOOOM)
Half Life - Magnum
Half Life 2 - Gravity Gun
Doom & Doom 2 - Shotgun / Super Shotgun
S.T.A.L.K.E.R. (Chernobyl) - Vintar BC
S.T.A.L.K.E.R. (Pripyat) - Eliminator
F.E.A.R. - 10mm HV Penetrator
Fallout 2 - Gauss Rifle
Deus Ex - Mini crossbow
Deus Ex HR - Pax 22
Assassin's Creed - Hidden Blade
Dead space - Plasma Cutter
Fallout New Vegas - Tri-beam laser rifle
Serious Sam - SBC Cannon
Unreal - Flak Cannon

For some reason the first thing that came to mind was the Dragon's Tooth Sword from Deus Ex. Makes stealth melee the way to go.
Second, Ellumyn's Bow from Arcanum, when used by Raven. Basically a machine gun, with boost vs. animals.
Possibly Master Sword in Gothic 2, good dex-based melee.
Enserric the Longsword from Neverwinter Nights: Hordes of the Underdark. Never thought of switching that out even if I found better stuff, upgraded as much as I could and stuck to it, him, whatever. I mean, one of the most interesting characters in the game...

I loved using the grenade launcher in Quake.

The Thief Series... My wits!
(I was often unarmed.)

Mind is the greatest weapon. (c)Psy-Ops: The Mindgate Conspiracy

I also like Ion Cannon from C&C.