I wasn't really into console gaming. Although at a time I've played 007 Golden Eye and The Mace on Nintendo a lot. To help the economy ;) I got the Xbox on the day 1 it was released in US, and a few games. No questions asked, Halo is the #1 game. For the record, unless you play HD game on HD TV you're missing all Xbox is about ;)
Halo - Still #1 Xbox game so far. Graphics is very good, soundtrack is excellent. It's a very interesting Sci-Fi shooter. Unlike
may other games this one actually has very interesting plot. Already played on normal and legendary levels, still playing from
time to time. Too much fun, and the deathmatch is very cool. Back in the days, online Halo sucked, there was no dedicated gameserver
and if you played with someone using the tunneling soft somehow there were always delays, lags, whatever... Spoils all the fun.
Well, now you have xbox live and huge dedicated community.
By the way, if you still haven't you should read the prequel to the game, Eric Nylund's book The Fall Of Reach. Ideally you'd read the book first and then play the Halo. A lot more interesting that way.
Dead Or Alive 3 - It would be just another fighting game if not the platform. One of the best graphics I've seen on Xbox. I'm not a fan of Karate games, but this one is fun. Very realistic graphics and physics as well. Also it features several different fighting styles and interesting combos. Sure there are half a dozen hot chicks with big, bouncy boobs, which is part of the entertainment too. Though during the survival match at very hard level you won't really have time to watch.