Parody is protected by law. But the question is, as Barrett suggests, can you afford the court costs?

Back in the 90s when Tim Nyberg and I were writing the Duct Tape books, we also did a bunch of parody of self-help / inspiration books as Bad Dog Press. One title, "When I am an Old Man I Shall Wear Mixed Plaids," was supposedly written by "Jerry Atrick" (get it?) and the "factoids" we presented were the work of the "Atrick and Associates Research Project" or "AARP." The words "A Parody" were right on the cover, front and back. The real AARP's lawyers sent me a scary letter, I replied citing parody law, and the lawyers phoned. They told me I was absolutely right, but that they were on retainer with the AARP, who wanted the book to go away, and were Tim and I prepared to fly to NYC and spend several weeks and thousands of dollars on lawyers to prove we were right. We didn't have that kind of money and had just sold out of the first printing so we simply changed the joke for the next printing. They were happy. 

So yeah, parody is protected--but if someone wants you to stop having fun with their original idea you have to have the $ to use that protection. And often a cheesy joke just ain't worth it.

On another note, at Book Expo in about the same year one of the creators of the "Chicken Soup for the Soul" series saw our parody ("Rubber Chickens for the Soul") and panicked on the spot, yelling at us that he was going to sue us out of business. His co-creator came over, looked at the cover, and said "This is a parody. I can think of no greater homage." And then he thanked us and gave us some free books.