Nth Killing Floor 1/2, Tripwire are the best when it comes to guns that feel good to shoot (and ESPECIALLY their shotguns). I haven't played a lot of KF2, but in KF1 the vast majority of my time was as support because the shotguns were absolutely fantastic. Hunting shotgun, AA12, combat shotgun, they all pack an incredible, visceral punch.
I'm not sure about the absolute worst, but Overwatch is definitely up there. Reaper almost feels like he's dual-wielding handguns, they feel so wimpy.
The hunting shotgun with all of its mods from Fallout: New Vegas. The moment I got this gun, it pretty much carried me the rest of the game and subsequent games after. It's so satisfying to shoot and send enemies flying.