Remixing video has become a popular cultural movement. We see it all over the internet where people re-purpose video to convey an alternative message. The Mister Rogers remix entitled Garden of Your Mind, produced by PBS Digital Studios takes hundreds of clips from dozens of episodes to create an inspirational song about learning. The audio of his voice is put through an auto-tuner to make it sound like he's singing.
This was made by professional producers, but remix culture is really a DIY movement and the tools are available for pretty much anyone who has a computer and internet connection. One relatively new tool that allows you to edit videos from YouTube is Easy YouTube Video Downloader, a free add-on from Mozilla that allows you to download videos from YouTube. It's an add-on which means that it creates an interactive button underneath the YouTube player to let a user download any video on YouTube. Once the video is downloaded, you can import it into a video editing program like iMovie or Windows Movie Maker to edit.