Zamzar, an online file conversion service, is an easy way to save a copy of a YouTube video on your Mac. To do this you enter the YouTube video’s address at Zamzar’s web site and it will convert the YouTube video into a file type which you choose, then send you an email containing a link to download the converted file.
Zamzar is actually a very versatile file conversion service. I’ve used it to convert Microsoft Visio drawings, Microsoft Works files and Microsoft Publisher files. To read Zamzar’s huge list of supported file types visit this web page. Zamzar offers several levels of service. Their free accounts are ad-supported. Free accounts are limited to processing upto 20 files per day which add up to not more than 500 MB. Paid accounts let you overcome these limitations as well as offering additional features.
Update: Here’s another possible option. Jaksta is a commercial application which claims to let you save a copy of any audio or video file that you stream in your web browser. I bought Jaksta and used it successfully a few times. I learned that it’s unable to download encrypted videos from YouTube. As of 2015, it seems that all of YouTube’s videos are encrypted so Jaksta has lost its usefulness for me.