In 1984, Prince became the first and only person to simultaneously have the #1 album, #1 single and #1 film in the USA.
February 2, 2007: Prince plays at Super Bowl XLI, performing on a giant symbol, busting out old mid-80s classics, and covers CCR and the Foo Fighters. All while rocking an aqua-colored suit. Billboard.com rated it the best Super Bowl performance of all time.
After years of distaste for Youtube and similar sites, and a poor sense of humor about himself, Prince released a single inspired by a Chappelle's Show skit at his expense, with Dave Chappelle dressed as him as the cover. Like the skit, the video also does not feature him in it, but instead has the video's (female) director/choreographer impersonating him.
Purple Rain, a rich, cohesive, concentrated blast of pop, funk and rock & roll, is the consensus choice, but the extended synthesizer jams of 1999 and the ambitious Sign '☮' the Times ain't too shabby either.
Batman is the best soundtrack for a movie based on a comic book superhero. Ever.
1995's The Gold Experience, the troubled release of which was surrounded by label turmoil, actually became a major fan favorite over time. It's filled with all kinds of groovy pop and rock workouts, and it's one of his last major statements before he went independent.
Really, pick any Prince album, chances are somebody will nominate it for this.