I got an X-Box not too long ago and I am just about finished with the two games I bought, Star Wars:Jedi Knight and Ailnt Hill 4. Between the two I like the Star Wars game better. I like games with a plot, not just fighting games.
Thanks,
Slee
Knights of the Old Republic.
Halo is very love-it-or-hate-it, with most people I know falling into the former category.
Morrowind: Gold Edition is worth getting, too (if you like RPG’s)… it comes with some fixes as well as the two expansion packs.
Project Gotham Racing 2.
If you liked Silent Hill at all, you can pick up Silent Hill 2 for twenty bucks. I thought SH2 was very, very good… better than 4.
Halo and Knights of the Old Republic were really the only two games that have made my Xbox worth it so far.
Sega GT 2002 was really fun for about 3-4 days. Too short though. It also pissed me off that I paid $50 for it when it first came out and then they started bundling it with new xboxes and it sells for $3.99 now.
Prince of Persia: The Sands of Time. Very cool and fun, and amazing graphics. Lots of story here and a fun ending. Not all that hard to finish, and limited replay, but an instant classic. At least rent it.
Halo, absolutely; a shooter with a decent (though not too deep) plot. Again, at least rent it, you may find yourself hooked pretty quickly.
Upcoming:
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Halo 2 (Nov 19) will be online multiplayer (cooperative and otherwise) as well as single player. We don’t know the story, it appears to be centered around the alien races in the first story invading Earth.
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Prince of Persia 2: The Warrior Within (Nov 16) looks like a winner, but also looks more combat oriented than the earlier one. Try POP:SOT first and see if you’re hooked.
Hey, here’s a good Game With a Plot: Beyond Good and Evil. I played this on PlayStation 2 last year, and it was quite fun and a great plot, with adventure and stealth gameplay. It was relatively short, but quite good with a satisfying ending.
Unfortunately, it’s only a year old but nobody seems to sell it any more on XBOX, despite great reviews. Hmmph. I see ebay has it in the $10 range. At least rent it, it’s a very good story-oriented game.
Fable. Infreakingcredible game.
Reviews, for your perusal: http://www.gamerankings.com/htmlpages2/516688.asp
Fable does seem worth checking out. I keep seeing it out of stock on the Hollywood Video racks, so I haven’t had my shot at it yet.
A more comprehensive review here.
Oops, I see Stark Raven Mad linked indirectly to the same review I posted. Apologies twice for redundency. 
BTW, sleestak: “Star Wars:Jedi Knight” doesn’t seem to be an XBOX game, but perhaps my game lists are betraying me; I haven’t owned any Star Wars XBOX games.
I see “Jedi Knight: Jedi Academy” and “Jedi Knight II: Jedi Outcast” listed for XBOX. Which game did you have?
Splinter Cell: Pandora Tomorrow. It’s seems to be another love it or hate it type of game. Personally, I love it. It’s got a decent plot, awesome graphics (the jaggies can get pretty irritating after a while but they’re not all that bad), and all kinds of cool stealthy moves. There’s really not that much fighting in the game since the idea is generally to stay out of sight, but when you do get some action it’s brief and intense.
Chronicles of Riddick: Escape from Butcher Bay. This game kicks ass in every way. Graphics are so detailed and lighting is so realistic you’ll do a double-take; absolutely the best graphics on a console. As far as gameplay is concerned, it’s a perfect mix of stealth, RPG, and FPS. You get guns, but you spend much of the time sneaking behind guards and snapping their necks or turning their own weapons against them. Yeah, the game is set in a prison, and it recreates the prison atmosphere darkly. Plotwise, your mission is to escape, but the journey is fun. All in all, an immersive game.
Don’t know what Jedi Knight game you have, but if you liked using Force powers check out Psi-Ops. It’s sorta over-the-top campy at times but I think that’s what they were going for. Combining psi powers like telekinesis with a realistic physics engine gives you plenty of creative ways to take out enemies. There’s a plot; it’s not too in depth but it’s enough to keep you wondering what’s next or what new psi power you’ll gain.
Have fun.
Infreakingcredibly disappointing. The designers delivered about 5% of their promises of what would be in the game, and you can beat it in ten hours. Doing all the side quests will probably push it up to twenty.
If you like being able to marry lotsa women, then Fable might be the game for you, but frankly, I’d recommend the Sims.
Halo, Prince of Persia and Beyond Good and Evil as mentioned before are all very good.
For the rest all games on the Xbox are crap. 
Games I own: Halo and Munch’s Oddysee, and I adore them both. I’m currently slogging my way through Halo on the “Heroic” level (2nd most difficult out of 4) and still enjoy the game very much, even after countless hours of replay. Munch’s Oddysee was a blast to play the first time, and so-so on the second time around. I highly doubt I will try and replay again, but it is a good game to have around for people who just want to futz around with the Xbox for the first time.
Games I’ve rented and liked:
Riddick- Escape from Butcher Bay - liked it, though the prison related sub-plots were not-so-hot.
Red Dead Revolver - Totally loved this game, and am considering buying it, even though I beat it while it was rented.