I would give a recommendation for Star Control II. While the game fairly humorous, the underlying foundation is quite a bit like Star Trek or Babylon 5, with races like the Scottish pterodactyls.
http://www.youtube.com/watch?v=ZAs7Ob_i_I0 System Shock 2 is definitely a RPG in my book, and no one can question the science-fiction aspect. I recommend getting both SS1 and SS2, as they are solid games that hold up to the test of time.
Iji is a freeware platforming game that has you controlling a young lady who has been altered with nanites. As you play through the game, you can tailor her abilities so that you can have superior firepower, improved protection, better hacking ability, and so on. Quite solid. Depending on how pacifistic you are, the protagonist may or may not become a psycho killer.
If you are willing to scrounge ebay and Amazon, you might be able to find a voice-edition of Star Trek: 25th Anniversary (DOS) and Star Trek: Judgment Rites, which are two licensed games that hold very true to TOS, and has excellent gameplay to boot. While you don't have RPG statistics, your performance is evaluated by Starfleet and a 100% rating boosts the strength of the Enterprise by a bit, which would be key to winning the final battle. However, you can make Captain Kirk be quite jingoistic and a rude military man if you wish, or figure out how to accomplish things in the Starfleet manner. Get these games if you want a genuine Star Trek experience.
If you are willing to wander further away from RPGs or the PC, then you would have more options when it comes to Sci-Fi games.
The first Homeworld and the standalone expansion Homeworld Cataclysm are not RPGs. However, they are top-notch examples of science fiction in my opinion. The first is basically about a migratory fleet, not unlike what we have with Robotech, while Cataclysm is a take on the Borg. (Though more similar to the Many.)
Shin Megami Tensei: Strange Journey - This game is for the DS, and the idea is that you are part of a military expedition to explore a region of dark space that is consuming one of the poles. The SMT series is primarily about the idea that all myths and supernatural beings are true - so we got Ashura, the Messiah, Tengu, Cthulhu, and the Flying Spaghetti Monster living in the same universe. Traditionally, technology and the supernatural are present in the series, and Strange Journey is no exception to that. Recommended if you like 3D dungeon-crawlers.
If you don't mind picking up a old console, I recommend Snatcher for the Sega Genesis/Sega CD. One of Hideo Kojima's earlier works, the premise is that Terminator-esque robots are killing people, wear copies of their skin, and replace them in society with the goal of accomplishing their master's will. Thankfully, the game has relatively short cutscenes when compared to the Metal Gear Solid games.
Star Control II
System Shock
System Shock 2
Star Trek: 25th Anniversary (DOS)
Star Trek: Judgment Rites
Iji
Homeworld
Homeworld: Cataclysm
Strange Journey
Snatcher