Tablet, stationary: Clash of Clans
Tablet, mobile: Ingress
With friends in Steam: Killing Floor (Linux), Rainbow Six Vegas 2, Alien Swarm
Solo in Steam: Star Conflict, War Thunder
Would play if had more time: Sid Meier's Civilization IV (Linux)
I have loads of Humble bundles bought, waiting to be discovered. They have been a great catalyst to release more games on Linux.
Game types are mostly co-operative FPS shooters with friends, tower defence with tablet, flying with planes or full 6 degrees freedom when solo. A mouse is a pretty essential controller in most games.