Parody is a fair use. That means, in a nutshell, that you can use something to make fun of itself without infringing on its copyright. This principle exists so that authors can't use copyright as a club to stifle criticism; without it, Mad Magazine wouldn't be able to use caricatures and exaggerated plotlines to show how bad a movie is, etc.
Now, satire is another thing altogether. A satire is a humorous work that uses one thing to make fun of something else, like Weird Al Yankovic's "Like a Surgeon." Weird Al has a bone to pick with the medical profession, not Madonna, so using her copyrighted "Like a Virgin" without her permission is an infringement. Think of it like this: Madonna isn't responsible for the excesses of the medical establishment; why should the fruit of her labor be used in a ridiculing manner without her permission?
It's amazing how many people just! don't! get! this! Once you've got the distinction, it's pretty easy to grasp. Here's a perfect example: The EFF has just released an high-larious Flash video of "Tinseltown Club," a parodical musical animation that uses the Mickey Mouse Club themesong to draw attention to Disney's involvement with the Hollings Bill, which will put Hollyweird's technophobic studio heads in charge of all new technology. This is a parody (we actually had to go back to the drawing board once or twice and make this more like Disney's own song and iconography, otherwise, the parodical link wouldn't be clear enough).
And it's fab. Got a Gnutella node or a Kazaa server? Put it up — the more, the merrier. In an age where everyone is terrified that if they utter the True Name of some big company's invention that they'll be sued into smoking rubble, it's way-refreshing to be able to shout the copyrighted words-of-power joyously and freely.
(Thanks, Ren!)