The "Inebriation" parody of the movie Inception (On YouTube here: http://www.youtube.com/watch?v=VsZ1SagUPb4) works because it is very well done technically and it stays very close to the style of the original trailers for the film (http://www.youtube.com/watch?v=66TuSJo4dZM). The makers of the Inebriation video were able to copy the cinematography, scene composition, and post processing effects of the original movie for their remix. Try running both videos at the same time to see just how close they were able to get to the original. Inebriation works because it takes a topic that is completely irrelevant to the original movie (a bunch of guys getting hammered) and uses the serious tone of the film.
Parodies like this are typically just for comedic value, but occasionally they are mixed with intense satire. The show South Park occasionally is able to do this, with their best example being the "Cartoon Wars" episodes. (http://www.southparkstudios.com/full-episodes/s10e03-cartoon-wars-part-i) The premise of the episode is that the show "Family Guy" is about to show a picture of Mohammed, and everyone in South Park has taken shelter to avoid any Muslim retaliation. During the episode the show the show goes over many of the arguments about radical Islam. They just happen to be told through a group of fourth graders.
Copyright wise both the Inebriation video and South Park are most likely safe. While both draw from copyrighted works, they both have enough original material to differentiate themselves. As long as a work brings something new to the original and does not simply attempt to reproduce the original it is safe from copyright claims.