The Xbox 360 HD DVD drive is capable of 720p/60*, 1080i/30, and 1080p/60 over Component Video and VGA***. Not sure about 1080p/24 support (although it is hinted at on the 360 website).
The Xbox 360 (Original) can support up to 1080p/60, for video games**, and either 480p/60 for SD DVDs (via Component Video) or 720p/60 for SD DVDs (via VGA).
The Xbox 360 Elite can support up to 1080p for games (via HDMI, Component Video, or VGA) as well as 720p/60 and 1080i/60 for SD DVDs (via HDMI).
*Formatting: (Lines of Resolution and Scan type) / (Number of Frames-per-Second)
**Theses are the specs of an Xbox 360 with the latest firmware installed
***The TV must also accept 1080p/60 via those connections or it won't work