Here's how I get stuff off of Youtube (or other similar sites). Watch the video, then go to the following folder: C:\Documents and Settings\<user name>\Local Settings\Temporary Internet Files. Sort the folder by "last accessed" (newest first), and the video file should be at or near the top of the list. It will ususally be a .flv file and larger than most of the others. Files from Youtube have names that are just a strange collection of letters and numbers and no extension, so just rename it and add the .flv extension. You can also sort by size (largest first) and video files will be near the top.
You might also need to check the "show hidden files and folders" option in view tab of folder options in widows explorer.
This works for Windows, but I imagine a similar approach would work for Mac as well. Just find where your browser stores the temporary internet files and it should be there.
Once you get the file, you can use any one of a number of tools to convert the file to whatever format you want.