My biggest issue with using a Mac Mini as a HTPC is that I can build a Phenom X4 (9550 -- good for transcoding if you want to move any videos to other platforms) with 4 GB of RAM, 1 TB HDD, 1 HDTV tuner, DVD-RW, on a new 790GX motherboard with HD 3300 graphics which will handle 1080p (though I'm not sure if the Linux drivers are yet up to snuff of accelerated decoding) for about $765 (if you keep to a budget case -- I'm in a situation to put the case behind a TV stand, so I don't care as much what it looks like so that has an NSK-4480B with its Antec power supply). You can get a nicer HTPC and power supply at correspondingly higher cost. Even with a fancier case (like say Silverstone's LC17 and Corsair 520HX power supply) for about $915. If you go with a 780G. Newegg has a combo with the NSK and a 9850 which can get you down to just under $710 even with the faster CPU.
Yes, both of the options above have a lot higher price than the Mac Mini, but they do have one tuner included and do have a ton more HDD space (so you're reasonably in the same price range as a Mini equipped to be an HTPC). I could probably cut the budget a bit by using multiple smaller HDD's, but I was just playing around with price. (I'm still toying with whether or not to replace my aging MythTV box and haven't decided to bite...yet.) And you are looking at a much larger machine. But, as I said, I'm looking at putting an HTPC in a spot where I don't really need to look at it. Of course, if you have a large flat panel that is not wall mounted, you can probably pull the panel out from the wall a little bit and put the case behind it.
On the plus side, the system above has expandability for more internal tuners, HDD's, and a discrete video card (well if you go with the 790GX, you could actually do Crossfire if you wanted to do serious gaming on you HDTV -- though I don't know the refresh rate on TV's but they seem to work for the consoles).
To my mind, the Mini is cute, but that's about the end of its list of virtues. It is saddled with slow Intel video and extremely limited expandability. So you're stuck with an external hard drive and external video tuner (though the first can be made to note take away from the aesthetics too much by the choice of the correct enclosure).