The Definitive Web Service - KeepVid
As I said, it's not hard to find a good website that will let you download YouTube video. The only real challenge is finding one that won't have malware-filled ads. I found KeepVid to be the best option for that; you can find the site at http://keepvid.com/.
KeepVid.com is a fairly standard service. If you wish to download a YouTube video, then you can just copy the URL from the page. Then go to KeepVid.com and place that URL into their bar at the top. You'll then just have to give it a second, and allow them to run the Java application to pull the download together for you.
The reason that I'll recommend KeepVid is because of their unique option. A number of download services just give you the .FLV file, which is not particularly useful. These files don't look very good, and you usually need a separate player to view the files, or a way to convert them into a viewable format. It allows you to download the files in .MP4 format. This format will work fine with any new version of Windows Media Player or Quicktime. There's no conversion required, you can just play it as soon as you download it.
The download times are a little slow, and you'll need to put up with a few ads, but the site itself is fine- simple and convenient- if you're looking to download something off of Youtube.