I don't think I can think of one single absolute favorite, but I know which weapons are my faves in the context of just the game they're in.
EYE: Divine Cybermancy:
This little fucker.Cawadoody Modern Warfare: The FAL. I like singleshot weapons like that, and it had that sick-ass reload animation. It's a shame I'm such a shit shot and can't properly use them.
Jaykin Bacon: Episode 2: I've never actually played, but it's a real tossup between the
handgun and the scoped knife.
Warband: One of the games I actually play regularly! In Native Multiplayer, I love: The Vaegir's Long Hafted Knobbed Polearm; The Nord's Great Long Axe; the Sarranid's Plated Quarterstaff; the Rhodok's Glaive and Poleaxe and the Swadian's Voulge and Rapier.
River City Ransom: Trash can best.
Star Ruler (Galactic Armory): Torpedoes best. Stick them on a million billion little bombers and swarm your enemies with rapidly-produced fighters from any planet, no standing defense fleets needed.
FTL: It's a tossup between delicious rapidfire ions and the glorious firebomb. CREW DEATHS, MAXIMUM SCRAP.
Dark Souls: I played some piddly wuss thief, but I really love giant weapons. Axe or hammer slightly preferable over swords, but Zweihander pretty sexy. In 2, I actually built properly for how I played, and stomped all the things with the Great Club.
Space Station 13: Fire extinguisher best.
Shadowrun Returns: Drones best.
Datajack: I think I had the... Jehrico? Some pistol, heavy rounds, 16 bullets, but I put a silencer and modified it to take bigger ammo, and it carried me pretty much the entire game. Essentially -completely- silent, but still enough punch to (eventually) put down a cyborg trooper.
Mass Effect: MIINNNDDD BULLETS. If those don't count though I really loved the heavy pistols.
DE:HR: Taser best.
In shooters I generally prefer a shotgun, because as mentioned, my aim is ass. I also like taking a huge machine gun, though. In games where my personal aim
isn't a problem, like Jagged Alliance, Silent Storm, or X-com, I like weapons with long ranges, though, because I can usually cheese the AI by sniping them.