Point-and-click (adventure) games

Blackwell Trilogy is awesome

Hands down Botanicula

King's Quest is really good if you don't mind that the games are very old and you'll likely need a guide for them because the puzzles do get hard.

The walking dead
Monkey island (There is a special edition on steam)
Indiana jones and the fate of atlantis
Sam and Max
Day of the Tentacle
Simon the sorcerer

Gabriel Knight!

Monkey Island series. I'm such a fanboy :3

Others have suggested it already, but I also say Botanicula. It's a cute/interesting game.

Deponia is cool

Sam & Max and The Walking Dead are both absolutely amazing. I've heard great things about Deponia as well, but haven't gotten a chance to try it yet.

The Longest Journey :D

Sacred Gold

Day of the Tentacle
Monkey Island series
Sam & Max series

Check the old dos games like Beneath The Steel Sky or Broken Sword series.