I've saved a bunch of my favorite YouTube videos by just adding them to my Favorites. I certainly don't have any special programs to do it. I think I run Windows 7 and whatever version of Internet Explorer would be the same vintage. I made a YouTube folder in Favorites and when I want to save a YouTube video I save it to that folder the way I save any other site. It must work because I go back and watch them regularly.
If there's some reason that doesn't work for you, you could just copy the addresses and paste them to a folder in Word, or whatever word processor you use, then reverse the process to watch them. It wouldn't be quite as convenient as having them in your Favorites, but it would be easy to do.