QuickTime Player will play the video, but to capture and save it, get QuickTime Pro ($29). When the movie is loaded all the way, click the downward-facing triangle at the bottom-right of the window, and choose Save As QuickTime Movie. Or you can try Ambrosia Software's Snapz Pro X 2 ($69 for the Movie Capture version).

Snapz Pro X 2 can capture any part of the screen - even a boring typing session - and save it as a QuickTime movie.
Tubesock
Submitted by rimglow (not verified) on Wed, 2007-08-22 14:50
Don't forget to check out Tubesock, for direct capture, from sites like YouTube.
Scrounging in the browser cache?
Submitted by mackerm (not verified) on Wed, 2007-08-22 16:12
Back in the OS 9 days, I used to look for the movie in Netscape's browser cache in the system folder. When I tried to do it recently, I discovered that the cache folder was divided into 100 sub-folders, making it impractical to find the big movie file.
Do any other current browsers make it easier?
With safari you can look in
Submitted by Stonedune (not verified) on Thu, 2007-08-23 05:52
With safari you can look in the activities window while at sites like youtube and download the movie. All you have to do then is use a program like iSquint to convert it for your iPod or computer.