What Star Wars fan would I be if I didn't mention the entire X-Wing series ?
X-Wing (the first game in the series, pretty hard even for experienced people, no reloading missions, but still, really fun and satisfactory),
TIE Fighter (you can fly as an Imperial pilot, ain't that enough ?

Besides, a good campaign and very fun to play),
X-Wing vs. TIE Fighter (the first game in the series to feature multiplayer, besides not much different from the two above),
X-Wing Alliance (nice plot, the Battle of Endor, lots of improvements over previous titles)
Wing Commander is like one of the first space-sims in the way we understand it, but it can be a bit problematic to run on modern hardware and OS.
Tachyon and Starlancer aren't really that great, but I'd give them a shot. Starlancer was quite nice last time I played it.
Freelancer - I really really liked the plot, even though it's more of an arcade shooter than space-sim, and the trading system plainly sucks.
And yet, Freespace (especially Freespace Open) can't be beaten by any of those. No other game has managed to make so perfect capship battles, so great atmosphere of danger (especially FS1). This is the only position where you actually feel that it's not a bunch of ships firing some single shots, but a freaking chaos, when you try to get a lock while flaks explode all around and enemies sit on your six.