Recently I wrote an article on how to auto replay videos on YouTube. One of the reader there wanted to know how to auto replay playlists.
My answer is, if she would have installed the Greasemonkey script and loopy, she would have got her answer :). The loopy plugin works with playlists as well ! Look at the image below, if you have loopy installed then you get the ‘Loop Playlist’ option:
Read this article to learn how you can install loopy.
One of the zillion uses of YouTube with loopy is :
Create your own playlist in YouTube, randomize the playlist, turn on loopy and start working out listening to your favorite songs 
.. that’s what I do these days !
Related Post: YouTube Video Auto Replay Firefox Add-On
Seems it stopped working with the new YouTube design
what now?
@Anders – You should press ‘loop playlist’ for it to start working.
Will it then loop the playlist automatic or should you pres this “loop playlist” first ?