YouTube videos are .flv files when saved. But how do you save them in the first place?

If you use Firefox, you are lucky, just install the DownloadHelper plugin (my version is 2.5.1). Now go to the YouTube URL with your favorite video. Let it load completely. Now click on Tools in Firefox, select DownloadHelper and you should see the file there. Click on it and download.

Or, there are online tools - try http://converttube.com

Now you are not there yet. iTunes will not work with .flv. So you need to convert it to some mpeg or avi. I convert it to MP4 using StreamClip (http://www.squared5.com/) StreamClip is especially good when you want to convert VOB files to MP4 and the VOB file audio is muxed. It seems it can also download/convert YouTube videos directly. So no need for the Firefox plugin if you are an IE fan!

Now that you have .MP4, just go to iTunes and Import this video into the library and sync with your iPhone/iPod.