HDMI is DVI with digital audio added - if you are using the TV's speakers instead of a receiver through a real set of speakers, HDMI is nice as it puts everything that TV needs in a single cable.
DVI is kickass digital cable - HDTV sources are all digital, so using DVI to a TV means the signal never gets converted to analog. So, this is a great option, usually the best one.
Component is the analog version of the top-end connection. It requires a bundle of cables (3) to provide the video alone, but it's the HD path for most people (DVI switches on receivers are brand new and only on high-end receivers, very few TV's have more than 1 DVI input, etc.). Doubtful you could tell the difference between Component and DVI/HDMI hookups...
SVideo is the next lower signal path, and Composite below it. NOTHING should be connected to an HDTV using either method if you care about the signal quality (such as a PS2, a standard VCR, etc. that really look like crap no matter how they are connected).