On YouTube, a lot of the legwork has already been done for you. There are playlists galore available for seemingly any interest. But if the user whose playlists you've come to rely on deactivates his or her account, deletes the playlist, changes privacy settings, or otherwise disappears from YouTube, you're out of luck. Instead of recreating other users' playlists, there is a handy Web app from Amit Agarwal of Digital Inspirations that lets you copy them to your account.
The app is aptly titled, Copy YouTube Playlists. On its page, click the big blue button to sign into your YouTube account. After granting the app permission to access your YouTube account, it will display a page with a box where you can paste in the URL of a playlist you'd like to copy to your own account.
When searching for a topic in YouTube, you can filter the results by clicking on the small Filters button below the search box. Choose Playlists from the filter options and then simply copy the URL of any of the search results and paste the link into Amit's Web app. Before you hit the copy button to add it to your Playlist collection, you can set the playlist as either public or private.
For further instruction, take a look at Amit's video on the topic: