After looking at different HTPCs, I bought an Acer Aspire Revo AR1600 (200 $, comes with keyboard and mouse (wired), Atom N230 CPU, 1 GB of RAM, 6 USB ports, eSATA port, HDMI port, ethernet (no WiFi) and nvidia ION LE graphics).
According to several reviews and reports I read, this model was said to be sufficient to watch even 1080p MKV videos. The load is taken off the CPU and put on the GPU, which reportedly allows the playback to work flawlessly, without stuttering or lagging.
There is a newer model of this nettop, the AR3610, which comes with a newer and faster CPU (N330), 2 GB of RAM, WiFi and wireless keyboard/mouse and costs 330 $. I was tempted to get this one at first, but then I thought that if the older model does the job, it's really a steal at 200 $.
I downloaded Ubuntu 9.10, put it on a USB stick (using unetbootin), booted from it, installed it on the HD (using the option "wipe the whole drive first").
Ubuntu booted without problems, the only thing that was (and still is) weird is that the outer pixels of what should be displayed on the screen are cut off. I tried different settings on the computer as well as on the TV, but it doesn't help. It's a bit annoying but it's not a dealbreaker. I probably won't notice these black bars when watching movies. (Update on that: The problem is caused by my TV, not by the computer. If I hook up my laptop to the TV's HDMI port, the problem is the exact same.)
I then ran the system update. (System --> Administration --> Update Manager)
Then I installed the nvidia drivers. The system asked me right from the start if I wanted to install the proprietary nvidia drivers, which I did. (System --> Administration --> Hardware Drivers)
The XBMC documentation says that compiz visual effects should be disabled in order for XBMC to work properly, so I did that. (System -> Preferences -> Appearance -> Visual Effects. Make sure "None" is selected.)
Then installed the Flash Plugin 10.1 beta release which supports the GPU (important for watching HD videos on Youtube for instance, without putting all the load on the weak CPU).
After all that was done, I installed XBMC:
sudo add-apt-repository ppa:team-xbmc
sudo apt-get update
sudo apt-get install xbmc xbmc-standalone
sudo apt-get update
(how-to found here)
This worked like a charm. XBMC has a very sleek and sexy interface and 1080p MKVs do indeed run without problems.
All in all: Thumbs up! 200 $ for a media center, small, quiet, nicely designed, I couldn't have asked for more.