When I'm just tired, I sleep or read books. My go-to game when I'm sick is Trine 1. I play it on a laptop sitting up in bed, fall unconscious, wake up and resume playing, and the laptop keeps me warm.

Congrats to:
You randomly win loadsa rep. Don't spend it all at once!

Just wanted to chip in with Saints Row 2. I've found that it's a game that you don't need to use a lot of brainpower for, and it's a sandbox game in many respects. You don't feel urged to do any particular thing at any particular time.