The wording of your question is somewhat misleading Raven since you're asking us both for the longest living and our favourite, which definetely aren't the same AFAIC.
That being said, I've tried many SF RPGs over the years, and only recently have I found one I really liked. In a roundabout kind of way, it could be considered the D&D of Sci-Fi too.
Basically, I was never much into hard SF. I liked Foundation, but I never got into all these other books from the same era depicting very technological and humano-centered universes.
So when I played Traveller and Space Master, the fun only lasted so long.
Then in 95-96 I found Fading Suns. I was hooked from the get-go. What I like in Fading Suns is the concept of the New Dark Age. It's a medieval futuristic society, if you will. There are noble jouses vying for power, an all-pervading (and not very open minded) Church with its Templars and Inquisitors, and a technologically minded merchant league that tries to keep its edge when the other two "big players" would gladly see them fall and plunder their tech.
Influences range from Gene Wolf's New Sun to Dune via Hyperion and a smidgeon of Warhammer 40k. When i say it could be described as the D&D of SF I mean that you can very easily view it as a medfan setting with demons, religions, magic (psi) and artefacts (tech), and this makes it very easy for D&D players to get into. Of course, there are a lot of further dimensions than what I'm describing here.
As an aside, you can check out the Story Hour I'm writing of my current campaign through the link below. Sorry for the mini-pimp.
Anothyer contender could be Jorune since again it combines medfan society with Sci-Fi elements. It's also a damn fine game well worth checking out...
