Component or HDMI for DVD player?

It depends on your display. I use DVI on my Pioneer Elite Pro 630 with Denon 3910 player and the picture is a lot better than component.

HDMI connections dont offer more resolution. They do allow digital video and audio to travel the same line-all digital audio BUT SACD!(in theory) Some interfaces-depending on the equiptment will only pass the video portion. The real advantage of the connection is that it avoids d/a and a/d conversions in the video and audio relms.
Some players offer what they call "upconversion". There are only 480 lines of "visible resolution" on any dvd produced yet. So, "upconverting" 480 lines to 720 or even worse 1080 is adding a whole lot of computer made up information(garbage) that probably will make the picture worse than a really good 480p chip set will make.
Dont get caught by the more is better and newer is better and digital is better with video signals. Most of the same rules apply to video as audio (I will not even mention the old vinal v/s cd war, we all know the winner of that one)Unless we are talking hidef...Which dvd IS NOT there YET!!!
So, I say try them both, look with your eyes and pick the one that looks the most natural-cable and resolution...

I have a very cheap($80 from Walmart) hdmi upconverting dvd player on a Panasonic 30" hdtv. The hdmi connection is visibly superior to the component connection, but when I upconvert the player to 1080i, I really see no improvement. I actually prefer to run it in 480p because the Panasonic automatically switches to a default high def color scheme(that sucks ass) whenever it sees 1080i. But the dvd player actaully has an incredible picture in 480p. I think it makes little sense to try and go beyond the dvd player's native resolution, especially when a progressive image looks so good, even if it is only 480p.