DoomRL has the best shotguns. There's one for virtually any type of combat, and are the main weapon used for corner shooting (sticking your gun around the corner, pulling the trigger and hoping. It's a pretty standard tactic). Highly modifiable, with a few good assemblies available, and plenty of good character builds dedicated solely to using them. Then there's the special/rare weapons, which are like this but even better. The Pancor Jackhammer is a glory to behold. They might not hit too hard at max range, but since this max range is off-screen for a fair few of them, that's not bad (and is a tactic in itself called radar shooting). They also auto-hit anything in their cone-of-fire, so anyone can use them, even if they do suck against armour (unless you're running an Army of the Dead build, in which case they're amazing against everything). A surprisingly versatile and tactical weapon, and one of the best implementations I've seen of shotguns in a game. Whatever you want, DoomRL has a shotgun for you. And a ridiculous amount of ammo for it too (which you'll probably need eventually). Seriously satisfying as a weapon. Any of them.
Another honorable mention goes to the original Syndicate shotgun. Not so much for its effect, but for its very cool sound. For me, that's still the iconic pump-action shotgun sound that everything else gets compared to.