Star Trek Online is an absolute gem. I am playing it for the last week since it became F2P and each day I am discovering a new thing that I like. You can even roam in your ship and in others! There is even ground combat and pvp!
And if you are a star trek lover, it doesn't f.up the lore for the sake of making a game, but bases itself on all the events happened in 4 star trek series (ToS, TNG, DS9 and Voyager), the ToS movies (like Wrath of Khan) as well as the 4 TNG movies and the new one (yes, even that one)
If you don't mind graphics, you can also go for Wing Commander 3-4, Prophecy as well as Wing Commander Privateer 2.
Also, the games suggested here are all nice.
You can also check Black Prophecy, if you are looking for online stuff. It is a bit different and takes time to get used to though.
You should try evochron mercenary. It's a new space game like freelancer that just came out last week. I looked it up and it seems to be pretty fun. I will probably pick it up soon, too.