HDMI also allows the TV to communicate with the cable/satellite box, Blu-Ray player, etc. Component video cables won't. Right now, that's not a problem with DirecTV, and thus, I have my DirecTV hooked to my TV with component (my TV only has one HDMI input). I have an upconversion DVD player hooked up with HDMI. If you want to get your upconversion DVD player or your Blu-Ray player to show HD, you have to use HDMI because the TV has to be able to tell the player it's legit. Otherwise, the copy protection will force it back to standard-def, even with Blu-Ray discs. Right now, DirecTV doesn't have that "feature" turned on, but I can't speak for Dish or whichever cable company serves your area.
As for sound... I'm pretty sure HDMI only carries stereo sound, not surround. In any case, you'd be using it to connect from the cable/satellite box or Blu-Ray player straight to the TV, which has two speakers in it. Then, you'd use either a coaxial or an optical cord to connect to the surround sound receiver to do your 5.1, 6.1, 7.1 or what have you.
Gonz has a point with the HDMI cable. HDMI is a digital signal that either works perfectly or not at all. Upgrading your HDMI cable will make no difference in picture quality at all. Upgrading an analog cable can make a difference, but HDMI, not so much.