I didn't have time to say this, but I love animated intros to live-action flicks, mostly because the companies who animate them put their heart and soul into it. At a scant few minutes, they know to make it the best animation, and always seem to sneak in cel shading and different cool effects. I just looked up the intro to "Troop Beverly Hills" (never seen it), and that might just be the best John K animation I've ever seen. Too bad they seemed to be a fading trend of 80's flicks, and rarely happen today. Though "Are We Done Yet" (2007) had one. (yeah, don't ask how I know that )...
The Nanny had an animated intro which I believe remained unchanged throughout the entire series. They also made a Christmas special of the show which used that style of animation.
Besides the Pink Panther ones, one of my all-time favorites is the animated intro to It's A Mad, Mad, Mad, Mad, Mad World (1963). And a choice animation-related bit of trivia related to it (via TCM.com):
So did Better Off Dead. Do the comic books from Mallrats and Chasing Amy count? The original Parent Trap and Freaked had interesting intros as did Catalina Caper and the LA Mr. Magoo. Adventures in Dinosaur City had some animated stuff, as did Ghostbusters 1&2.
Since tv shows are being mentioned here i figured id post the little-seen animated intro to punky brewster season 1: http://www.youtube.com/watch?v=S8gGUzpQgBI
(if this breaks the youtube policy please delete the post)