Recently I've been playing around with testing HD videos based on the H264-codec. For those who don't know, HD videos are video files with very high quality and resolution. The upcoming HDTV television standard is based on that (which is quite problematic due to the HDCP copy protection, but that's not the topic of this article).
Apple recently released Quicktime 7 to play HD mov files, Microsoft supports WMV HD videos in it's Media Player. HD videos are available in three qualities, 420p, 720p and 1080p.

For the system requirements of 720p-videos in Quicktime, Apple says:
2.8 GHz Pentium 4 or faster processor, At least 512MB of RAM, 64MB or greater video card
And even more for 1080p:
3.0 Ghz Intel Pentium D (dual-core) or faster processor, At least 1GB of RAM, 64MB or greater video card
As my system doesn't really fit these requirements (1,5 GHz Pentium M, 512MB RAM, 128 MB video card), I was quite impressed that I could run a bunch of videos in quite reasonable speed and quality with linux software.

Trying out various players the cvs-version of mplayer did it best for me. Pretty much every player available on linux uses ffmpeg for H264-decoding, so they should do all, but there have been a bunch of important fixes in ffmpeg recently and this is quite the easiest way to get a recent ffmpeg-version running.
Running mplayer with these options gave me the best results:
mplayer -lavdopts skiploopfilter=all -framedrop -fs [videofile]
-fs is for playing the video in fullscreen (you don't want to play HD videos in a window), -framedrop let's mplayer skip frames when your system is too slow (else it will be out of sync very fast, some framedrops don't really hurt). About the -lavdopts skiploopfilter=all, I don't really know the details of video codecs, as far as I understood, this disables some steps in the decoding that shouldn't be needed on most videos, but can result in wrong decoding. I couldn't see any differences, it improves the speed quite a lot.

Now I could play all 420p and 720p videos at pretty reasonable speed. I especially liked this BBC one showing african animals and landscape. For the 1080p ones, it differs. This Trailer for "The Island" runs pretty well, others don't.

Bugs: Some videos cause mplayer to crash. On my radeon, the mplayer xv output has a problem with the large videos (width of 1900) displaying a pink block on the right side. I've written bug-reports and hope those things get resolved soon.

To sum it, I'd call linux pretty much "HD ready", beside some small issues it plays the HD stuff very well and with impressive performance.

Places to get HD videos:
Microsoft WMV HD Content Showcase
Apple HD Gallery