I know that for an NVidia card I can
sudo apt-get install nvidia-current mplayer, reboot, and then use
mplayer -vo vdpau -vc ffmpeg12vdpau,ffwmv3vdpau,ffvc1vdpau,ffh264vdpau FILE.mkv to get accelerated video playback of H.264 and other codecs, so even full HD videos can be played back with only little CPU. (And there are many other options, e.g. XBMC also supports VDPAU.)
But how do I get accelerated video playback if I have a recent ATI or Intel video card on Ubuntu Lucid? How do I figure out if my video card has acceleration built in? The solution has to work with mplayer or mplayer2. It's OK for me to recompile mplayer(2), but I'd prefer installing both the kernel and the X.org X server from a binary package repository.