Here's a few:
http://www.youtube.com/watch?v=ZcFqJGps4pU Chicago: Stay the Night
This is a classic from the eighties, back when MTV actually showed music videos. Music videos were a lot easier to find back then; it's only been recently with the advent of YouTube that one can see music videos; throughout the nineties and up until just a few years ago, they were next to impossible to see. This one is one I remember; it's story-driven, and not just another band playing music on stage. It's a perfect example of how I'll love a music video even if the song isn't neccessarily a favorite.
http://www.youtube.com/watch?v=EjAoBKagWQA Bjork: All is Full of Love
Let's go a step further. I'd have never noticed Bjork as a musician if it weren't for her videos. With these astonishing images, however, one pays attention.
http://www.youtube.com/watch?v=3MHBIoGh6Og The Flaming Lips: The Yeah Yeah Yeah Song
You guys introduced me to this one; there's another post around here somewhere a year or so back that introduced me to this one. It features an appearance by one of our favorite mythical shapeshifting organisms.
http://www.youtube.com/watch?v=omFdpnSu57U U2: Beautiful Day
On the other hand, when a favorite band does something visually spectacular, you get a great treat. You already showed us "Vertigo." "Beautiful Day" off the album right before it is similarly stunning, though it relies less on spectacular effects and more on plain cinematography, showing the artistic beauty and magic of something as seemingly mundane or even frustrating as an airport.
Taking a Gestalt approach, since it's the "in" thing...