Whenever a conversation about HD and the 360 comes up, I see a ton of confusion about which outputs give you 1080p. Hopefully this handy chart from DanielN will help to answer a few questions.
Xbox 360 connected using componentDVD’s via HD-DVD drive: 480pDVD’s via DVD drive: 480pHD-DVD’s: 1080iGames: 1080pMCE Extender: 1080pMCE Extender for OCUR PC: 1080P
Xbox 360 connected using VGADVD’s via HD-DVD drive: 1080pDVD’s via DVD drive: 1080pHD-DVD’s: 1080pGames: 1080pMCE Extender: 1080pMCE Extender for OCUR PC: 520P
Xbox 360 connected using HDMIDVD’s via HD-DVD drive: 1080pDVD’s via DVD drive: 1080pHD-DVD’s: 1080pGames: 1080pMCE Extender: 1080pMCE Extender for OCUR PC: 1080P
The only other thing you need to check is what resolutions your TV supports on each input.
[Update] Thanks to MattG for pointing out that the new Premium boxes contain HDMI as well.