Dragontape is an online video mixing tool that allows you to take videos from a site like YouTube and merge them together to create one large video. Dragontape would be a great way to merge together several clips to show your students without having to go back and forth and save to a playlist.
Dragontape uses a simple drag and drop feature and you can search for YouTube videos from within the website or you can copy and paste the URL. Organizing and watching the videos is very simplistic as well. You can register for an account, but it is not necessary to use the software. Registering does allow you to save your video mix tapes that you create.
You can give your "tape" a title and determine whether you want it to be private or public. Go here to get started creating your own video collage.