First, run out and get Fallout and Fallout 2. They’re the best Science Fiction RPGs ever made, and you shouldn’t have any trouble running them on a modern PC.
Next, Star Wars, Knights of the Old Republic. You can even get the sequel, though the fact that at some point they seemed to stop bothering to try and make the story make sense will probably piss you off.
The Buck Rogers games from SSI were great, and despite the age of them, they make a good showing on the short list of science fiction RPGs.
Anachronox is a fun console-style RPG with a lot of humor.
System Shock 2 and Deus Ex were designed in first-person shooter style, but they are also genuinely RPGs.
Albion is a nice RPG, if you can get your hands on it, though I never finished it because the premise got kind of stupid as the game dragged on. ("I.e., the Celts were the glory of the human race, great warriors while not being war-like, until the ‘Heliromers’ – the Greeks and Romans – came along and taught the world to hate.)
Arcanum – Fantasy/Steampunk. It had both fantasy and science-fiction elements, and was brought to you by the people who made Fallout. The graphics seemed primitive even by the standards of its own time, but it was excellent in character development and story arc.
Septerra Core – Great story, console style, somewhat tedious in how missions ended up as crawls through mazes searching for switches that opened up more maze. Overall, I’d recommend it. The story was great.
Maximus XV – Diablo clone in space, not recommended unless you want to keep your hands busy while listening to an audiobook.