There's actually quite a range of space-based MMOs, but I've played three space games quite extensively and will talk to those:
A) Time of Defiance is BY FAR my favorite for three reasons:
1) You're in space with a LARGE group of others, and the map IS HUGE! (I.e. it is NOT POSSIBLE to make it from one side of the map to the other in four days!)
2) You're not just one ship, but you build an entire FLEET of a wide variety of types, and the AI MANAGES ALL THE BUSY-WORK FOR YOU. (I.e. you can pre-assign them a task, start one or more building, and when they're done they just start doing their job(s)! Even if you don't tell them what to do they figure it out on their own if you want! (Hence it's not all "busy work" like the following game.... )
3) If you look around enough on The Net' you can find "coupons" for a free trial that lasts four or more days. (AHem: I once stayed up FOUR DAYS STRAIGHT playing this game.... ) [See post(s) below. Alas, ToD is no more....]B)
Homeworld is the remainder of a world on a ship that's trying to flee an enemy that is set upon destroying your entire civilization.
Short summary: I grew tired of having to micro-manage the dozens of simultaneous battles in what is an already VERY difficult game in the first place.
Also: It is NOT an MMO, it is an RTS, and to my memory it is NOT free.
C) Of course there's always
Spore, which is much more than a space game, but turns into one "in the end." Everything I now discuss is about Spore's "Space Stage" endgame.
Spore has a unique presentation in that it is a combination of an MMO and RTS all-in-one. Over time COPIES of races built by other players are slipped into your copy of the cosmos, so while it's not actually RTS, it does have the possibility of infinite variety. Likewise to ToD, it's playing field is HUGE.
Spore is also, NOT free....
That's all I have to offer, sry!
...Although now you've made me want to give Time of Defiance another go!