I'm glad that everyone was so quick to correct the misconception that you would still need separate audio cables if you use HDMI for your video. It does indeed run both video and audio, and quite well too.
I just recently compared component and HDMI in my setup (46" Samsung LCD TV, upsampling DVD player [to 1080i], and an XBOX 360.
As far as audio goes, there is a definite improvement from the standard red & white "RCA" cables to HDMI. Clarity is better, imaging (the ability to envision the placement of the sources of the sound) is better, and there seems to be better support for the mid-range sounds as well.
As for video, in my setup HDMI is the winner without question. I simultaneously hooked up the component and HDMI cables to my upsampling DVD player. Using the THX Optimizer program as a guide, I adjusted the picture settings to the best quality possible for both sources. I was then able to compare rather quickly simply by switching sources on my TV.
I watched several movies, both live action with CGI and computer animated (Matrix, Finding Nemo, Monsters Inc., King Kong, Chronicles of Narnia), and the difference was astounding. With the HDMI cable, detail was better, contrast was more dynamic, colors were represented more accurately (which is surprising considering this WAS one of the strengths of component cables), and there was much less "noise" in the picture. I found the same to be true for my XBOX 360 at 1080p.
While I don't have a next generation DVD player (HD-DVD or Blu-Ray), I can say without question that for upsampling DVD players and video game consoles, HDMI is the way to go. But ultimately, it's a matter of opinion. Try hooking both sets of cables up to do a simultaneous comparison for yourself.