My Co-Workers and I have been playing tons of DiRT: Showdown, Sonic & SEGA All-Star Racing and Gauntlet on Steam. We are kind of getting tired of those and are in search of more of these games. We have done emulators but always go back to the mentioned games because of optimization reasons. I decided to seek help on GOG before checking out Steam in case there are some hidden gems. Can you guys help us out?

What we are looking for:
•4-player games (more if possible as I've seen, we default to USFIV for 2 player so nothing less than 4 ktnx)
•Playable Offline
•Controller compatible (means no having to map to keyboard for any kind of function)

Thanks for absolutely any suggestions.

Hammerwatch matches all the criteria and I think it has been part of this sale. (You might still be able to get it on discount)

Crawl
Crimsonland
Hammerwatch
Rayman Origins
Devil's Dare
Megabyte Punch
Octodad
Risk of Rain
Shadowgrounds series
Spelunky
Trine series -> just 3 players

Aside the aforementioned, there are also:
Dustforce DX
Fist Puncher
A Fistful of Gun
Giana Sisters: Twisted Dreams
Moto Racer 2
Towerfall: Ascension
Worms 2 (Hot Seat)
Worms Forts: Under Siege (Hot Seat)
WormsWorld Party Remastered (Hot Seat)

Pixel Junk Shooter is co-op... but that's a little low from 4 player...

I think Whacky Wheels.
Ring Runner is also Co-op (sorta)

People already said the ones I wanted to suggest on GOG (except Divinity Original Sin EE, weren't they planning to add 4 player coop on same screen ? But I may be wrong) so it will be outside of GOG (in case it can help you) :
Jamestown
Broforce

I don't think anyone mentioned ScreenCheat yet....