When a game is set in space, invariably it's set there so you can fly a spaceship and shoot at things. Space Engine does away with all that nonsense, leaving you with just... space.
Billed as a "free universe simulator", whether you call it a game or not depends on how much you like exploring (and shooting things, I guess). But once you download the 400MB file, you're free to explore a procedurally generated universe at your own page, with the whole thing designed to give you an idea of how vast deep space really is.
It's definitely relaxing and had me reaching for some Jon Hopkins CDs. But seeing how smoothly it pans out from Earth only makes me want to see this kind of technology applied to something with a little more to do.
Space Engine is free, and you can grab it at the link below.