A couple of suggestions... Mass Effect was pretty good. Kind of lost its way on the second game, but more or less got back on track by the third game, even if the ending did suck as bad as everyone says.
You might consider Xenosaga. It's sort of a space opera RPG for the PS2 (you didn't specify PC or console). Despite having swords, Disgaea for the PS2 and PSP is EXCELLENT! It's a bit of a level grinder at times, but it is friggen hilarious, even if some of the humor is a bit juvenile. Might be a bit more fantasy than sci-fi, but it's funny, and who can say no to exploding penguins? I also like the Deamonic Senate, where you can bribe people to vote your way, or just beat the crap out of them and force them to do what you want.
On the PC end of things, Final Fantasy 7 for the PC was just given a minor refresh to make it compatible with newer systems, and I think is being sold on Steam. It does have swords, but it's also set in a kind of modern times, plus you get to beat the crap out of some corporate executives, so I consider that a real bonus.
Star Craft the original and Star Craft 2 I can recommend quite highly. WarCraft 3 was okay, though the human levels are always kind of whiny.
I also liked Dawn of War, which got me started on reading the Warhammer 40K series of books. The first Dawn of War was a pretty classic RTS. If you're not familiar with the Warhammer 40K universe, a lot of the plot won't make any sense, but it's still a pretty fun game. The Winter Assault expansion pack was kind of worthless, but the Dark Crusade and Soulstorm expansions were both excellent even though they have only a paper thin plot. Dawn of War 2 was more of a tactical RTS, where you have a couple squads of soldiers, and you need to use them to complete various objectives. Dawn of War is basically set in the 41st Millennium where humanity has created an empire spanning virtually the entire galaxy, but is constantly under threat from various alien races, as well as daemons and evil gods, so there's this race of genetically engineered super soldiers known as the Space Marines who are kind of the elite troops of the Imperium that you play as. That's just a very brief synopsis. If you're familiar with Dune, Warhammer kind of borrows heavily from Dune, and then has been expanding on it for the last 20-30 years.
If you can find it, despite being a FPS, the original No One Lives Forever was also excellent. Think sort of like the Austin Powers movies, only without having to listen to Michael Myer's make a bunch of really bad jokes. It's sort of like a spoof on the James Bond movies. The first one was hilarious, the second one improved the gameplay a lot, but at the expense of almost all the humor. In the first one though, you just have to make sure to take the time to be stealthy, because there are a lot of really funny conversations you can overhear. One of my absolute favorites is two members of this criminal organization having a discussion on the sociology of beer and criminal behavior. Or there's one where a couple of scientists are discussing the implications of using heavy water when making zombies. And not to give too much away, but there's a discussion between an American and Russian on a space station about whether 3 fatalities in a month is normal. Not to mention all the funny intelligence items you can find on the way. Maybe not strictly speaking sci-fi, but it has elements of sci-fi in Bond-like gadgets.
Gears of War was actually kind of an interesting twist on the FPS. Not sure if it was necessarily the first, but it was one of the first to use a cover system, where you take cover along a wall, or duck behind a slab of concrete or something, and then kind of take turns shooting at the enemy and being shot at. Wasn't really sci-fi or anything, but it was a solid action-adventure kind of game.
That should be plenty to keep you going for a while.