I'm going to stick with modern era stuff-there is a good reason why you might want to go back and hit some classics (specifically, Tie Fighter), but a good run-down would look like:
KotOR/KotOR2 - I'd definitely play the first one first, and the second one is a pretty good game too. Smart RPGs with a good mix of action and an even better emphasis on dialgoue and character development. Had a lot of fun with both.
Republican Commando - Another console port/simultaneous release, but hey, that's Star Wars. Lightweight and a lot of squad based fun without the boring nonsense that usually accompanies squad based games.
X-Wing Alliance - Yes, it is not the best of the Star Wars space sims. It is decent and it does look OK and runs on current machines without resorting to DOSBOX trickery. Worth playing, got a bad rap at release for no real reason and never was able to shake it.
Jedi Outcast/Academy - For a bit more of a original trilogy feel. Outcast is a good FPS on its own merits, and more traditional in nature than Republican Commando. The saberplay is nice in those games too.
Lego Star Wars - Fun game. Don't judge this book by its cover.