(UK only, obviously)
In Firefox's about:config, set general.useragent.extra.firefox to iPhone.
Load a show in the iPlayer.
Run this bookmarklet: iPlayLater
You should then get a prompt to download the file.
It's just over 200MB for an hour-long programme, so please don't abuse the privilege. As Ian Forrester says, it should ideally be easy to stream the shows in any player without this kind of hack (one of the main reasons for doing this is that the streaming Flash player doesn't switch off the system screensaver like VLC does, so the screen goes off every 15 minutes).