As Jid noted in the News Articles section, the BBC has now made available software for Linux and Mac users to download iPlayer programmes. However this makes use of proprietary software from Adobe with DRM. For those (like me) who prefer not to use DRM there is an unofficial DRM-free alternative with
get_iplayer.
I installed get_iplayer on my Debian Lenny system using the instructions on the site, and it was straightforward, with just one unsatisfied dependency which I installed from the normal Debian repository. It's a command-line program, but very easy to use, and has more features than you can shake a stick at. The programmes are downloaded in Quicktime format, and can be viewed with several Linux progams such as Mplayer, Kaffeine and Xine.
If I can summon up the energy after Christmas, I'm going to look at writing a GUI front-end for get_iplayer, but in the meantime it works very well in its command-line form.