I've done that, but resolution was an issue
I have an LG 32" LCD HDTV, and I occasionally hook my mini up to it using a DVI to HDMI cable (available for cheap, BTW, from cablesforless.com). It works just fine, but the resolution issue was not quite so straightforward for me. The TV and the Mini both support a variety of resolutions, but the only one they seem to like to do *together* is 1024x768, which is not fantastic. Both the computer and the TV can do better than that, but there doesn't seem to be a higher resolution than that that they have in common.
Still, it's nice to have a computer available in the living room. I think I may ultimately dedicate the Mini to this use, and get a BT keyboard and mouse and store them in the coffee table. Could be a nice convenience.
I would like to use this set up as my 'media player', including DVD player. Problem with that is that the TV doesn't support the various aspect ratios in HDMI mode that it does in TV mode, so you can't zoom widescreen DVDs to fill the screen.