Dire Straits releases their hit album Brothers in Arms, which includes the song "Money for Nothing". The video, which included then-groundbreaking computer animation, caused jaws to drop in amazement the world over when it hit MTV. The video took two weeks just to render using a Bosch FGS-4000 computer. This was years before anyone even thought of the idea of texture mapping, and if you look closely at the CGI parts you can see where they cut some corners by using some scenes twice (but reversed), using static images, etc. Completely understandable given the technology available at the time. I don't even want to hazard a guess at what it cost to produce!
Fast forward to today. Check out this amazing video for "So Cold" by Breaking Benjamin, created entirely using the Half-Life 2 engine. First off, the song rocks and the video both kicks ass and captures the mood of the game beautifully. Amazingly, it was done using captures straight from the game (there are no pre-rendered cut scenes in HL) and additional animation done using developer and mod tools that are freely available on the net. The G-Man's mouth and facial movements match the vocals perfectly thanks to Valve including a library of phonemes as part of the Source engine.
The whole thing is done using a standard PC.
After zensidhe sent me a link to that video I found out that there's an entire subculture (for lack of a better term) on the net that makes similar "machinima" videos. (You've probably already at least heard of Red vs Blue.) A lot of them seem to use the Source (Half-Life 2) engine, which makes sense. If seeing the G-Man sing hard rock isn't your thing, how about a geekier version of him singing "Stacy's Mom" by Fountains of Wayne, or Alyx Vance singing dance pop? :-)
Finally, it's not a music video, but this Rube Goldberg machine video shows the most convoluted means of killing a headcrab zombie ever devised. Fun stuff.