I don't want to be a Debbie Downer here but I think HDCP should be mentioned.
In short, yes you can view HD signals without using HDMI... for now.
HDMI connection is meant to carry digital video and audio signals all in one cable. Unfortunately the entertainment industry wants to protect their media from piracy and thus HDMI is also capable of sending HDCP (High-bandwidth Digital Content Protection) signals over the HDMI cable. If you have a TV or Monitor that is HDCP compliant, then you need not worry. If however you are planning on getting HDTV programming from your local television company and your HDTV set only supports hi-def via component (analog), you might not be able to view it at full HD resolution. If HDCP is enabled via your TV provider, the hi-def signals get downscaled to DVD quality over the component input. If you are planning on buying a blu-ray or hd-dvd player, ps3, or even some upscaling dvd players, the HDCP signal via HDMI becomes an issue.
Many older HDTVs also have a DVI-I port which *may* support HDCP signals since it is a digital interface. You just need a HDMI-to-DVI cable. DVI does not support audio though so you would have to hook that up separately.
This may not be a problem now (as there are many people that currently view HD programming over component) but unfortunately HDCP is the future. Google "HDCP" and "Image Constraint Token" for more info.
If you are a gamer, consider your current options:
Xbox 360 (no HDMI port) + HD-DVD = 720p, 1080i/p over component.
PS3 (built-in blu-ray player) + HDMI cable = 1080p content properly displayed as it is HDCP compliant.
PS3 (using component cable) = blu-ray movies downscaled to dvd quality since component cables are not HDCP compliant.
Now I have read of HDMI strippers that you can buy, but have no idea if they work or not.
With the arrival of Windows Vista and HDCP compliant video cards, HDCP compliant computer monitors will soon follow. I believe there are some out there already but are not applicable for our use as they are too big.
As far as I know there is only one 15" LCD TV that is HDCP compliant and that is the Philips 15PF5120/28. It doesn't have a HDMI port but it does have a DVI-I port which can do both digital and analog. The Philips website claims that it is HDCP compliant over DVI. Of course you would need a dvi-to-hdmi cable but those are no problem to acquire. The other 15" HDTVs like the older Philips/Magnavox do not have a digital input. Only analog via component and VGA. If you consider building your projector as a great investment of both your time and money like I do, you may want to consider future-proofing it for HDCP.
The future is unfriendly.