So you're thinking about getting a 360? If you get these games, you'll have a hell of a lot of fun.
Advanced Warfighter: Great single player, great online, and good local-multiplayer, this game also really shows off the 360's graphical power.
Oblivion: An awesome RPG; another way to show off the 360's graphics. Only single player, but this game is addicting.
Call of Duty 2: Amazing single player. Although tough on Veteran Mode, this is still a fun game to play. It will get old, though, unless you have at least 3 friends, or Xbox Live.
Project Gotham Racing: Great sim. racing game. Nice graphics, awesome cars, addicting game. Racing fan? Pick this up.
Saint's Row: Last but not least, Saint's Row. Granted a GTA rip-off, but this is an amazing game that will hold out well until GTA IV is released in '07. Definitely buy this.
Stay Away From:
I'm sure you'll be tempted, but don't even think about buying these 2 games:
Tony Hawk's American Wasteland: It's the same game that was on the XBox and PS2 versions. There isn't even a graphical improvement; if there is, it's hard to tell. It's a good game, but if you've played it, don't bother with the 360 version.
Madden '07: This game has the graphics, but not the gameplay. This is a downgrade from the PS2 and Xbox versions and it costs more money. Stay away.
Buy the 360! It's a great buy. $300 - $400 sure, but it's well worth it.