Originally posted by: MeBeJedi
As I was pondering this question, it occured to me - since DVD is a component video source, the component video connection would be outstanding, but does a given DVD player keep the video signal in its digital form for transfer through the digital outputs (DVI/HDMI)? If so, then you would get a purer signal between the player and the display device - i.e no digital->analog conversion inside player to analog->digital conversion inside the display device. (Do any current analog TVs have these digital inputs? I would guess no, but I wouldn't put it past a manufacturer to include one just to impress the customers.
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As I was pondering this question, it occured to me - since DVD is a component video source, the component video connection would be outstanding, but does a given DVD player keep the video signal in its digital form for transfer through the digital outputs (DVI/HDMI)? If so, then you would get a purer signal between the player and the display device - i.e no digital->analog conversion inside player to analog->digital conversion inside the display device. (Do any current analog TVs have these digital inputs? I would guess no, but I wouldn't put it past a manufacturer to include one just to impress the customers.

DVI is basically digital RGB. DVD players with DVI outputs first convert the video on the disc from its digital component colorspace into digital RGB, and that's what is sent to the display. Enthusiasts who know the difference consider a component > RGB conversion a downgrade because color information is lost. Some people still prefer an analog component video connection over DVI because they feel the color is superior on some displays.
HDMI is compatible with DVI because it handles digital RGB. However, HDMI is also capable of carrying a true digital component signal. Some DVD players with HDMI outputs support digital component output. I can't think of any displays off the top of my head that accept it, but there may be some. There are some high-end scalers that accept digital component via HDMI because it's preferable to work in the original colorspace during deinterlacing/scaling even if the signal is finally converted into digital RGB before being sent to the display.
It's possible to hack the DVI standard to carry digital component signals, but it's messy and non-standard.
And yes, there are many analog displays (CRTs and CRT projection TVs) with DVI and HDMI inputs.