I'm typically a pinpoint-accuracy guy, but the shotguns in Left 4 Dead and Metro 2033 (Last Light's weren't quite as satisfying) really did win me over. Left 4 Dead 2's combat shotgun's an absolute beast of a firearm.
Halo CE' M90 (or the M45 if youre playing CEA) 8-gauge shotty was a scary weapon. Easily the best weapon to kill the flood and foolish covies alike. It was also the best of the series. THE M90II and M90B practically only have a third of the range (the M45 in reach and the Mwhatever in 4 and 5 are good overall, but I'd take the og CE boomstick anyday)
My favorites are Gears of War Gnasher, DMC4 Coyote-A and the triple barrel shotgun in Bulletstorm. Also, I don't know if they count as shotguns, but Bloodborne's blunderbuss and the spear rifle are pretty cool.
I'm biased. Doom has been said but I'm going to vote specifically for the single-barrel shotgun. The super shotgun has that fantastic feeling of impact but I almost always found myself using the single barrel over the double. Power and speed.
I like the DOOM 3 shotgun, but the problem with it isnt it's range or the sound imo. It's the god awful random weapon spread. Sometimes the gun with 1 shot in close range, at other times it takes 2 to 3 shots. I'm talking point blank right in their faces.