Sure, everybody's linking to Ironic Sans' (admittedly entertaining) Celebrity Patents, since Waxy pointed them out, but did you know Prince actually has a real patent?
Patent D349127 is for a portable electronic keyboard musical instrument. But Prince prefers to call the monstrosity the Purpleaxxe™.
It's a horrible 80s-style keytar, though it wasn't created or actively used until well into the 90s. Prince, of course, didn't inflict the ungainly shoulder-mounted funk launcher on his own frame -- he made his then-keyboardist Tommy Elm play it. But no, this sort of humiliation wasn't enough for Prince to inflict on the young man, he also renamed the poor fellow Tommy Barbarella, after -- you guessed it! -- the 1968 Jane Fonda sci-fi cheesecake flick. As you might guess, it's one of Prince's favorite movies.
Though the Purpleaxxe™ has fallen into disuse in the interceding decade and a half, Elm is still saddled with his unfortunate sobriquet (joining such stalwart Prince-named talents as Carmen Electra). And you can find mention of the Purpleaxxe™ in various liner notes on Prince's albums, as well as the lyrics to a b-side remix on an out-of-print CD single from 1992. You know, if you're in to that sort of thing.
Well, a real design patent. Not exactly the same thing as Hedy Lamarr's invention of spread-spectrum communications, but at least it's a patent.