Hello,
my girlfriend and I love adventure games, so usually we solves the puzzles together (it's more fun that way),
but I was thinking if anyone could suggest other types of games we could play maybe?
Maybe turn based games, two player action games or such?
any good experience and recommendations?

Trine, perhaps?

Heroes of Might and Magic 2 and/or 3 both have hotseat multiplayer I believe. You might want to check if the King's Bounty Games have it also. I'm not sure. Someone in the relevant game forums could tell you if they don't come along here and confirm this.

Worms!

Worms has hotseat multiplayer too, incidentally I'm playing it with a couple friends right now, but that's more of a competitive experience.

Hm.. That's the only one I can think of....