Fan Fiction Fun

I’ve noticed a lot of the self-published books that really take off start out as fan fiction (Still trying to figure out the 50 Shades/Twilight connection but that’s a blog for another day.) I have a friend who writes great fan fiction about science fiction/fantasy shows she watches and has a large following. I’ve never really read much fan fiction but perhaps I should start. Do you seek it out? What is your favorite?