Space games I am playing atm:
1) Starbound (early access game still in development, but still having loads of fun in it. Think space version of Minecraft).
2) Sins of a Solar Empire (4X Space game)
3) Endless Space (+ Disharmony expansion) (4X Space Game)
4) Galactic Civilizations 1 and 2 (Another 4x space game)
5) Sword of the Stars Complete Collection and SotS 2 (more 4x space games

)
4x is the general "explore, expand, exploit, and exterminate".
All but Sins, if I recall correctly, are Turn based. Sins is RTS.
I've heard X3 (depending on version) is a lot of fun (newest or such, is apparently absolute shit). But, don't have X3 yet and don't have time for it