The simplest utility to download from YouTube that doesn’t require you to install anything (not even Java) is a service called ClipConverter.cc. All you do is copy and paste the YouTube URL containing the video you want to download and follow the simple instructions. It’ll even allow you to convert to other formats. Once in awhile, the service may get overloaded and you’ll just have to try again later.
Other free tools I’ve tried and worked well include:
If you have another tool you prefer, feel free to suggest it below in the comments.