Family Guy actually has a lot of non-parody parodies. For example, they had to have permission from Lucas to collaborate on the Star Wars "spoof" because a lot of it wasn't even a parody, it was just them in Star Wars costumes and storylines.
I saw on youtube these American Idol finalists doing the Tom Cruise scene from Risky Business. It was basically just a complete re-enactment plugging an advertisment in the middle. I'm pretty sure they had to have permission to do that first, because it doesn't constitute a real parody, and apparently a lot of people found it funny. I thought it was stupid because it was just a shot-for-shot remake.
People don't have to be original or creative to be considered funny. Seeing someone do something out of context can be funny enough.
You get scenes from Family Guy that "should not" be funny but are simply because it is animated. Every episode now features these long drawn out scenes of something trivial happening for 30 to 60 seconds as a gag. It's funny simply because of the characters doing it, and the fact that you don't see that kind of thing in animation very often.