Just discovered that YouTube has perhaps my favorite "live music on TV" moment ever--it's Moby, Jill Scott and Blue Man Group from the 2001 Grammys. Sure, the Grammys pretty much suck by definition, but you can always count on one or two performances that offer a thrill, and every couple of years you get something like this. I recommend viewing with headphones or, alternately, PLAY FUCKING LOUD1.
1Apologies to Bob Dylan.