I bought an Xbox 360 for Christmas, and while setting it up I was kind of disappointed to find that my only display option was 480p. As it turns out, you can switch to HD mode, but it requires that you replace the included Composite cable with a Component or HDMI cable.
Microsoft offers a Component cable, which has an Xbox 360 AV connector on one end, and Component (Red, Green, Blue, Yellow, Red, White) connectors for audio and video on the other end. Newer Xbox 360 models also include an HDMI port, and you can connect them directly to your TV with a standard HDMI cable. The HDMI cable will send both video and audio to your TV, but you can also send audio through to your stereo or home theatre with a separate AV audio cable.
Once you have your cable connected, go to Settings > System > Console Settings > Display > HDTV Settings from the home screen. You should now see options for 720p, 1080i and 1080p (some may be disabled depending on your TV capabilities). If you went with the Component option, and you still don’t see anything but 480p, make sure that the TV / HDTV switch on the cable is set to HDTV.