My favourite scifi game is Mongoose Traveller right now. It is a system that has very little setting in the corebook and is a game based around space travel and the varying lines of work a space traveller may find. There is fluff books that expand on it's default setting called The Third Imperium, but lots of people just make up their own fluff and use the system. Noteable for having fun life-path character generation, spaceship design rules and also a system for generating random planets and also sectors of space to go travel with your designed ship.
The Void is another space-faring game. Pay what you want on Drivthrurpg, which means you could get it for free if you wanted. A standalone game based off the Chthonian Stars supplement for Traveller, I can sell it in one sentence; 'Literally the film Event Horizon: the RPG'. Made to place Cthulhu mythos in a lower tech Traveller setting, a more hard scifi take where character's are restricted to our own solar system. Has a similar system to the GMC rules update of Nwod, but uses d6s so successes crop up more. Makes your character feel pretty boss, though they'll be less equipped than Traveller characters, giving a more Survival Horror aspect. A character tends to need to choose between that pistol or the bullet-proof vest when grabbing gear as an example.
Eclipse Phase is another to recommend. It's Creative Commons, the devs actually have a free download of the corebook on their blogs if you look for it. Post cyber-punk and mainly set in our own system, though in a post-Singularity future (also there is a Stargate riff on some worlds opening up the game to extrasolar locations). Uses a percentage-based system and has an incredible amount of freedom of what characters you can play. Unique in that your character for the most part can download their psyche onto a black box that can be swapped to other bodies, including Uplifted animals and robotic bodies. Lots of factions with varying politics, space travel is less of a thing on ships, characters tend to do a STL download and upload of their ego to whatever world they want to go to.
Firefly currently has it's own rpg series out now. It uses the Cortex Plus system, using a dicepool mechanic where higher sided dice represents better skill in certain categories. Has a fairly simple and quick stakes mechanic too, where the defender rolls up first to make a DC and the attacker has to beat the stake set.
Numenera, it's like a D&D game done through the lens of Heavy Metal and Moebius painted scifi fantasy. Has a feel similar in parts to Dune and also the comic series Saga with how weird the world is. Set on Earth literally one billions in the future (how it's not swallowed up by the sun by then is handwaved by mentioning some tech from a past civilisation is stopping it doing so), mankind is now the ninth civilisation to walk the world. They live on one huge super continent, only the South-Western part is mapped, though the map and area covered is huge. Lots of relics from high-tech past ages are out there to be found or people already have put them in use. I can't talk much about the system as I've only played it once. The setting is great and really inspirational to writing however.