The Star Wars X-Wing/Tie Fighter Series was a favorite of mine back in the day. Similar, though not as good.
-X Wing Alliance
-X Wing vs Tie Fighter
All released for PC, the first three on the list were released a few years ago in a set called X-Wing Trilogy. The original X-Wing and Tie Fighter were released for DOS, so Lucasarts did sort of a WKS thing to bring them up to date. X-Wing Alliance in particular is an excellent game.
Uh oh, I won't get in trouble for reccomending SW games on a WC forum, will I?
While there is no "replacement" for wing commander, i personally think that the freespace series is awsome. Not so much a personal story as you have no player character, but the over all war story is quite good and i personaly find the gameplay to be just as good as wing commander. Prettier too considering they are both newer games. (If i recal correctly there are actually some people trying to import wing commander ships into the Freespace 2 engine.)
If you havn't tried this game yet you really should. I was huge wing fan until the stoppped making them. There is an online space MMOG called Jumpgate (www.jossh.com) I played it for 4 years before giving it up for Starwars Galaxies. (i have superstar destroyer with my name on it) Its a great game with many different thing to do. I think it was designed to be wing/privateer online before origin got chopped up by EA, but there is no official statement for that. Give it a try I bet you'll be hooked like I was for many years.