Reccomended is a 2.7ghz C2D IIRC. It doesn't need a terrible lot of power to record, but if your video card doesn't support the right codec in hardware on playback you might need that.
If you even care about playback, locally.
It all depends on what you're looking for, but when a $90 AppleTV, $160 Boxee Box, and $50 PBO all have more than enough hardware, I'd be pretty surprised if even older machines couldn't muster up enough to do a single playback at one time.
The best use, to me, for a media center box is in the closet - with PBOs, AppleTV2s, or similar hooked up to each TV. I don't want to deal with the noise of a PC in the living room.