I ran a tivo in the states, and I can tell you that it's a wonderful gadget to have. There is a project called mythtv out there now that does all that and more now, well worth checking out:
I'd like to put one of these together in a mini ITX and just use it with my LCD screen to watch telly etc on.
Another really sexy way to do this is to locate a cheap dvd player that has an IDE DVD drive in it.. easier said than done perhaps.. but you take out the guts of the dvd player, hook up the ITX board inside and leave the IDE DVD drive in place, looks rather nifty. I even know of folks who've re-connected the LEDs to make everything look like a normal player!
I also recall that some of these mini or micro ITX boards have a bios that will play a dvd or music cd/mp3 cd-rom right after POST if it's detected, I thought that was a very cool feature too
DB