Given a YouTube or Vimeo URL, downloads the underlying video file, with a sensible file name. It downloads the highest resolution version of the video available: first it tries HD MP4, then regular MP4, then WebM, and finally FLV. It also works on playlists, and works as a bookmarklet[doesn't exist] to download the video you're watching.
Back in the day, I had been subscribed to so many YouTube channels that they didn't have the functionality to show me all of the new videos.
I'm also seriously annoyed with having videos and channels "go missing" because of takedowns, bannings and closures. YouTube doesn't even give you the author or name of a video when it's removed.
The solution was to locally cache at least the basics of the information. If I had my way, all of the videos would be downloaded too, but that's too extreme even for me. I also think my ISP would have a fit.