OK here's the deal:
You need to be able to put the controller/mouse down at any moment in the game and walk away without penalty (lost progress for not saving doesn't count, I mean within that play session). No multiplayer-only games. I want to play alone for these.
Let's take Puzzle Quest for example. On the map, in the menus, during a battle, during dialogue, and everything else there is nothing "active." At any moment you could walk away for two hours and nothing would be different.
To clarify, this does NOT apply to games like FTL and Sim City. Those game can pause and send commands, yes, but there is still action in which you may need to work on the fly. Don't ask why. In the words of George Carlin "These are my rules, I make 'em up."
I ask because I've played a lot of stressful games lately and honestly I just need something to chill with. It's a mental thing for me to know that there's never any pressure ever, and it's really important when I'm trying to play something relaxed. Board games are really good for this, but it's hard to find one that's fun playing alone.