Here you goes
HDMI is not required for HD etc, it has all cables (Video and Audio) in one small cable. The "expensive" ones are usually Monster, but you can get similar quality (at 1080p its hard to tell anyway) with cheaper $20-60 brands. HDMI will only give you HD and Surround sound *IF* your Surround Sound Box supports HDMI. Plugging it into your TV will only give you 2-Channel (Stereo) audio and HD.
Component [Y'PbPr / Red Green Blue] is my preference, although it only goes to 1080i [some do 1080p I believe] , its still very powerful and cheap. Its cheaper than HDMI (over 50% cheaper in most cases) and give similar quality. You will get one cable that splits into 5 ends, 3 are video, 2 are audio (or something like that) Component is also much more supported than HDMI as you can use it as a Composite cable also.
S-Video is kinda-sorta sub-par. I've never gotten it to work 100%, but basically its the same quality +/- 25% than Composite (Standard 3-plug RCA cables)
The Composite are the worst other than coaxial, but most older TVs use em.
Coaxial is standard for getting TV to your TV Tuner or TV, but again, its the lowest quality.
If your using a Xbox 360 your best bet is using Component Cables (comes with 360) and a Optical Audio port. Optical meets if not surpasses HDMI audio quality, and its p00nage
DVI - few TV's have DVI, since its a rare-er cable, and its slightly expensive, but if your TV has it, it will give you Computer-Like Quality (usually max resolution = 1080p, but DVI supports much higher)
VGA - currently (other than elite) the only way to get 1080p on the 360, but VGA is another powerful cable that will give you Computer-Like visuals that will not only be able to get 1080p, but go higher, its only limited by your TV, as most VGA cables/systems get up to a large amount
Anyway, basically if you want one cable, and your Surround Sound box supports it, HDMI.
If you want to get similar quality for cheaper, Component + Optical
If you want standard (480i) quality, s-video and lower