Although there are several free video downloading services available online, videos can easily be downloaded from YouTube by using just Safari and a free video conversion utility.

Open Safari, then browse to the YouTube video you want to download.
When the video starts downloading, click on Safari’s Window menu, then choose “Activity“.

The Activity Window that appears will list all files loaded from the website. Find the entry with the largest file size (it will be several Megabytes in size), and double-click on it.

Safari will open its Downloads Window and start downloading the file you double-clicked on as “videoplayback.flv“.

To convert this Flash Video file to a movie file, open it with Quicktime Player X and select the File menu, then choose “Save As“. Enter a file name for the video, set the format (“Movie” for MOV, “iPhone” for M4V), and click on the “Save” button.
If you need to convert the video to another format, you can do so by importing the MOV or M4V file to iMovie or a video converter like VisualHub and exporting it from there.