Let me chime in on this subject.
HDMI is a digital connection that was finished by December of 2002 which is very new compare to other video/audio connection.
HDMI - can carry up to 5 Gbps of digital information. Support both RGB and YCbCr sampling. Also can carry sound alongside with video in one cable. Cable is about the same size of 6 pins firewire...
DVI - only tranfer digital information up to 1.65 Gbps. Support only RGB color that means YCbCr have to be converted to RGB before send to the cable. Does not support sound. Cable is bulkier than HDMI...
Component Video - is analog connection. Only support YPbPr, that means if the information is RGB. It must be converted to YPbPr before it send to Component Video. Require 3 seperate cables...
of the 3, HDMI is the best imo. Its digital, can send the highest digital information, take up less space and support multi-channel surround sound digital audio.
Just for fun, might as well include firewire and USB 2 ports too.
Firewire - can send up to 400 Mbps and like USB are universal, it can send anything beside video/audio, such as computer data.
USB 2 - supports up to 480 Mbps and it\'s flexible and bi-directional like firewire too. It also support anything digital beside video/audio just like firewire.