I don't even run my 360 through a HD tv for 90% of the use I get out of it.
The only way I get the HD effect is to take it upstairs and connect it via the VGA cable to my monitor and put the sound through the PC.
one day I'll get a HD tele, but at the moment it's good enough for my lesuirely sessions when I've a few hours free and want to blow off some steam.