As you can maybe guess, I'm really tired right now since I have only slept about 7 hours over the last 2 nights put together. This happens from time to time when I get stressed out over something I need to do that is difficult or tedious to do. Usually once I do whatever needs to be done I can go back to getting a good nights sleep.

Anyway I will not bore you with my sleeping habits here but my problem is that it gets hard to game when I'm really tired and hence I would love to hear some good suggestions from you as to what games you play when you are really tired? I can't really play FPS because my reflexes are for shit and I can't really play RTS because my brain is mush - so what genre or specific games do you play when suffering from insomnia?

Any type of turn based game or anything with a "pause and command" option works. This happens to me all the time.

STARS! is a nice one especially if you are mid-game and already have your mining routes up and automated.
The Contraptions games here on GOG are great so long as you avoid the expert levels.
Card games are also great. I've got a great Dogs Playing Poker game that looks great and simple enough to play; also anything solitaire is easy enough.

Saints Row (2 or 3) can be fun just to run around town a bit when you're tired.

Anything turn based (HOMM, Age of Wonders, Fallout) when you're too tired to have quick reflexes, but still are able to - more or less - think straight.

Civilization 4: Colonization or Civilization 3

Dungeon Crawl Stone Soup

Free as well!

Here!

Mostly games that you can play only with a mouse. Heroes 2 and 3 do it for me, it's like going through the motions without thinking while still being fun.

Strategy, tower defense and hack n slash games come to mind as relaxing and not to demanding.

Silent Hill 2

It is a nice and silent type of game. I would totally recommend it to someone who is tired

Killing Floor

Point and Click games are nice

I played Botanicula recently while tired and stressed and enjoyed it immensely. It's a game that requires no skill and it presents a world that is quite charming and unique. It made me smile more than once.

I love Civ games but find them overwhelming when I am tired because they require too much of my time, and when I am tired it's usually because I don't have time (that is, because I have too much work).

Majesty always works for me.

Desktop Dungeon is cool to, although it plays more like a minesweeper game :D

Amnesia or Penumbra, always fun when you're tired.

I find old Lucas Arts adventure games to be very relaxing. Try playing some Monkey Island or Day of the Tentacle.