Hello there.

An old friend and I are looking for a cool game here on GOG that we can play Co-op over the internet, preferably the main campaign or whatever the equivalent is and something that saves our progress, be it in the form of a save game in the storyline or a character or so.

I've tried sorting the catalogue by co-op but I don't think that's the full picture.

Has anyone got some nice suggestions?

I'd recommend Sacred Gold if you like hack'n'slash.

why not try out the serious sam series here they have excellent co op, provided you like the game

Not a GOG game, but Titan Quest has really good co-op.

Thanks for the tips, I'll look into them. We used to play Serious Sam Split Screen in the summer holidays on one keyboard, that was amazingly annoying but fun!

I play co-op every once in a while with my brother. Not on GOG, but I can recommend:
I've played both Serious Sam and Sacred in co-op and both are really really fun.
Sven CO-OP mod for Half Life 1. Probably the best co-op experiences I've ever had. Immense fun.
Any hack and slash is fun really, so maybe try out Diablo II?
From shooters, Quake II is a solid choice.
Recently we bought Rainbow Six: New Vegas, or whatever it's called. If you liked the game, it's not a bad choice.
Also got Frozen Synapse, but have yet had to try it.
If you have Starcraft I/II or Warcraft III, try some tower defence maps. Make sure you find one for two players though, otherwise they can be too easy / too hard.
Arcanum has a fairly fun multiplayer map - if you own the game and know how to play it. I wouldn't really recommend buying it just for that though.

This is all I can think of for the time being, I'll let you know if anything else springs to mind.

edit: also, my brother played the new? Tomb Raider platformer in co-op with a friend and he said that it's one of the best co-op experiences that he's ever had.

edit2: oh and Carmageddon also has some fairly fun multiplayer modes, i.e. tag

Seconded!