You definately do not need to be familiar with the source material to enjoy the rides. It will help you get some of the references and inside jokes, but the rides will still be entertaining.
I have never watched the Simpsons but love the ride. Even though Jimmy Neutron is now gone that was another that I never saw and still enjoyed.
As for the person who talked about PotC and HM (Country Bears)...the rides came BEFORE the movies, so they were designed to be a ride and therefore are not good examples to prove this point. That would only make sense if you were asking if you can enjoy the movies without ever being on the ride before! (Soon to include Jungle Cruise and BTMRR)
Better Disney examples would be Star Tours, ToT, Tom Sawyer Island and the Swiss Family Robinson Treehouse etc etc etc . Again, all enjoyable without the source material but better when you can link the references to the source.