The popular Firefox extension AdBlock Plus now filters requests made by Flash. In "Open blockable items" they show up with "object subrequest" in the type column. This allows you to obtain URLs of Flash videos which are accessed using http. You can simply right click on that line, "Open in New Tab" and get a download dialog. If the video is already loaded in the player, the "download" typically comes from the Firefox cache so it's fast and bandwidth is not wasted.
(I'm using Firefox 3.0 and AdBlock Plus 0.7.5.5. Note that Flash can make other requests besides just those for the video and there are other ways to show videos (besides loading FLV files via http). However in most cases, http is used and it's easy to save the video. For those who don't want to do it themselves, there are services like KeepVid.)