A satisfying weapon, for me at least, needs to sound good above all else. Battlefield: Bad Company's weapons sound like the mutt's chutneys (especially the XM8, even though I hate the actual weapon), but they don't have much stopping power so they do fall a bit flat.
A weapon that 'clicks' with me is one that I can hold down the trigger at the exact moment my opponent does, and shred him first. It needs to be accurate for long-range shots, but also a good bullet hose when fired from the hip so that it does CQC well.
Shotguns, if animated and audio'd well can also be the most satisfying weapons in any game. A loud 'blam' followed by a shower of blood, a 'clump', and the smooth, satisfying sound of the pump action racking back... drool.
All of this is of course futile if the weapon takes an entire clip to drop somebody, something many game developers need to understand.
A few of my personal favourites:
Counter-Strike/Source's M3 - headshots with this thing are just orgasmic.
Crackdown's semi-automatic homing rocket launcher - for obivous reasons...
Battlefield Vietnam's M16 and XM177E2 - sounds are great, animations are excellent. Both can drop a man in two shots.
Rainbow Six Vegas's MP5A5 - felt more like a knife than a gun because of its quick, agressive sounds and rate of fire. Great on burst mode.
The Getaway's Glock 17s - auto-aim made it a little easy, but popping somebody with lead with these was great fun.
Crysis's SCAR - as crap as Crysis was, the SCAR was a nicely rounded weapon with satisfying animations and good sound.
Crysis's MPX8 - sounds fantastic, but that's it.