Google Groups per Reggie, thanks.
...
As you probably found, this is not a standard feature of Picasa web.
As this is a regular question, I looked around a bit and wrote this little how-to that should help you out:
1) You need firefox, so if you don't have firefox installed yet, you can finf it here:
http://www.mozilla.com/en-US/firefox/new/
2) Start firefox and install the plugin DownloadHelper. It allows you to download movies and you can find it here:
https://addons.mozilla.org/en-US/firefox/addon/video-downloadhelper/
3) You need to restart Firefox to complete the installation, and afterwards go to picasaweb (picasaweb.google.com)
4) When you go to a page with a movie, there is an icon at the top-left corner of the firefox window that "wakes up", and becomes three globes turning around. Push the arrow next to it, and click on the line sliding down.
5) Now you can save the movie as a .flv file...
6) But... this type of video file can't be watched in most kinds of video software, including Picasa :-(... so you need to convert it. Install par example this little tool: "FLV to WMV Convert", you'll find it here: http://www.lumixsoft.com/download.php
7) Start the tool, add the .flv files you want to convert, pick the spot where you want to put them... and push "Start".
Remark: with the Plugin "DownloadHelper" you can convert immedaitely to other formats as well, but this isn't a free feature (he puts in a logo)...