You absolutely need to have HDMI. Might not be an issue if you never do anything but play 360 games in HD via component input, but if you ever plan to watch HD movies then you need HDMI. Both Bluray and HD-DVD are expected to mandate HDMI if you want to view their product in high-def due to copy pretection concerns. Plus, as more and more network and cable switches to HD, expect the networks to start enforcing HDMI-only connections for their high definition content.
PS - Jimmy, what's HDMI?
The simple answer is that it is just a type of video connection that is pretty close to being standard on HDTVs.
It allows digital-to-digital video transfer from the source (cable box, console, or DVD player) to the television. The other alternative for high resolution signals is component connections (red, blue, and green cables) which is an analog signal path.
Theoretically you will get a better, cleaner picture via HDMI since you have none of the losses associated with digital to analog conversion. In practice, however, the difference is pretty negligible for quality products using decent component cables.
The big deal about HDMI is that it allows the use of HDCP, which is basically a form of copy protection for video signals. Piracy has become a huge, huge concern for content providers since the advent of HDTV and they are very serious about only providing HD signals over avenues they can "control"- copy protection via HDCP. Consequently, it won't be long until they will block HD signals over component connections since they can't implement copy protection on it.
Anyone in the market for HDTV should not consider one that only offers HD via component connections.