Favorite Space RPG? That's a toughy. The problem is, when you say Space RPG, I don't think Star Wars / Star Trek / Serenity / etc.
When you play those, you aren't playing a Space RPG you are playing Star Wars or Star Trek or whatever. It's somebody else's universe with already established rules of behavior and what can or can't go on (and loads of canon to back them up). You aren't really playing a Space RPG so much as an RPG that happens to occur in space in your setting of choice.
When you say Space I tend to think of exploration and discovery and and exciting adventures on strange worlds that are free from things like Prime Directives and Jedi Orders and people with Magical Police boxes. There isn't anything wrong with those when you want to play in those universes, but it doesn't, to me, allow the level of freedom you get with things like D&D and Pathfinder and so on. You are constantly bumping up against the already established 'heroes' of those universes in one way or another directly or not.
Also, a good Space RPG means more to me than just being on a foreign planet. A Sci-Fi setting doesn't automatically make it Space. Sure, you can go to a new planet and spend lots of game time there and be perfectly happy, but the option has to exist for you and your crew/friends to completely pick up and go elsewhere just because you can. The latest edition of Gamma World, for instance (at least as far as I have been able to play it) isn't a Space RPG necessarily. You are, more or less, on Earth. You can hop about a bit between various versions of Earth, but it still doesn't seem like it qualifies as a Space RPG. (Although, yes, you can go to the moon, so maybe it qualifies just barely.)
Star Frontiers was the first RPG I ever GM'd so I'll give it a nostalgia vote and also say thank you for the above links. It's been a long time since I've done anything with SF and I appreciate getting to look at it again.
It interests me that no one has mentioned Spelljammer. I've not played it, but I have heard stories. Are they true? Is it horrible?
The best Space adventure I ever played in was run off the Big Eyes, Small Mouth system. I can honestly say more fun was had doing that than any other Sci-Fi/Space game I've played to date. It was a lovely game system that allowed you to do almost anything you wanted in terms of both genre and character. As long as you had a good story in mind you could build any set of characters, powers, and equipment you liked to go with it and take it any direction you liked.
Traveller I've read but never played. Couldn't convince the group to go for it, much to my everlasting chagrin. It looks like the kind of thing I could go for, but it just never came together for me.
Ditto Space 1889. Always wanted to play, never got the chance. Someone still makes it, do they not?