I use a freeware program I downloaded from downloads.com - which is a site run by CNET magazine.
It's called YTD Video Downloader. It has a section for downloading videos from sites like YouTube, and it also has functionality for converting from any of its supported file types to any of its other supported file types. So, I typically download a video, usually in MP4 format, then I typically would use the conversion functionality to convert the MP4 into MP3, so that it creates a nice MP3 song file from the downloaded video.
For YOUR needs, you could convert from MP4 to AVI, or whatever other format you desire.
Go to
http://download.cnet.com/windows/ and search for YTD Video Downloader.
All software from that site is guaranteed to be virus free, BUT the install process usually attempts to have you do things like download and install Chrome, various toolbars, etc, so MAKE SURE that you look for check boxes for such bloatware and remove the checks.
Other than that, you are good to go. I use YTD Video Downloader ALL the time.
Bob Bone