I'm running it on Vista. Home Premium. It is very temperamental though, mostly at startup. Often I have to try several times to get the game to start working, receiving a "Kotor 2 has stopped working" message soon after clicking on Game from the game menu. It has also stopped working similarly a number of times from within the game, but it's hard for me to know how much this is Vista and how much it's the game itself, which is undeniably very buggy.
Incidentally, I had the same problem with GTA 3, except that only started once, then never again.
So there's not much I can suggest except just keep trying to get it to run. I'd give it about 10 tries in a row before giving up. Once you get into the game it runs well enough to be worth the hassle.