Mitch Hall points to the best Downfall parody ever: Hitler upset by the copyright infringement notices against the Hitler Downfall parodies.
The folks who made Downfall have to know that they've earned tons of free publicity from the parody videos and that millions who otherwise never would have watched the movie found out about it via these parodies. Either they're complete idiots in wanting them taken down, or they're reckoning that the additional publicity from the take-down notices is worth the reduction in parody videos.
Of course, Peter Cresswell presumably will refrain from watching the video above as the owner of copyright wishes that his IP not be used in this way. Sorry you're missing out, Peter; this one's hilarious.
Update: That last bit wasn't entirely fair. Peter supports fair use provisions.