UPDATED: FAVORITE ANIMATED MUSIC VIDEOS - NOW INCLUDING GORILLAZ

Here's what an old fart I am: I can actually - clearly - REMEMBER a time when Mtv simply didn't exist. I remember it being invented. Crazy.
Anyway...
Music videos are an interesting phenomenon... most of the time, they're just marketing tools, but every great now and then, someone seizes the opportunity to embrace it as another form of artistic filmmaking and transcends the medium (for those of you who are struggling artists, take my advice and look for ANY opportunity in casual conversation to use the term 'transcends the medium'... it makes you sound all artsy and intellectual and you'll get an arts grant).
But, as usual, I digress...
When you approach music video as a 'multimedia art piece', it's easy to see why some of the most innovative directors/musicians choose animation as a way of providing a visual accompanyment to the music... in animation you can literally control every single image and every nanosecond of the timing.
For instance, if you're shooting a live-action video and you choose to have a scene outdoors, you can't control how the wind blows or what shape the clouds take... of course, sometimes this is precisely what the director WANTS for a sense of immediacey and a 'naturalistic' look... but, if you're trying to 'say' something very specific with your video, animation allows you to control the shape of every could and the speed at which it moves... the leaves on the trees in the background obey your commands... they can stand PERFECTLY still (something else that is virtually impossible in a live-action scene) or sway in a breeze of your creation... you could do a scene where trees swayed 'menacingly' if you wanted.
Anyway, with this in mind, I present to you 3 animated music videos that I can watch over and over and over and over ad infinitum (and, yes, I'm too stoopid to know how to actually post these videos here - so just cut and paste the links into your browser if you wanna watch the videos. Or don't. I won't lose a lot of sleep over it either way).

Gorillaz - "Clint Eastwood"
I'm filled with shame that I forgot to include this in the original post. I have no excuse, but let's move on with our lives, shall we?
Now, the fact that Jamie Hewlett came up with an animated pop band is enviable in and of itself, but let's just focus on this particular video...
This video is an absolutely brilliant example of what you can do when you actually COMBINE different animation techniques instead of relying on any single element to be the "star". You could technically classify this video as LIMITED animation with the sheer amount of re-use it utilizes.
When this thing came out, I simply could not stop watching it, taking the time to watch it repeatedly frame-by-frigging-frame.
http://www.youtube.com/watch?v=qpDer9wdUEw

Linkin Park - "Breaking the Habit"
The animation styling and art direction on this are so gorgeous I could watch this all day and never stop loving it. Not a wasted line. Not a wasted movement. Very deliberately 'anti-slick' yet clearly created with absolute precision and purpose. I also dig the song a lot, but it's the only Linkin Park song I'm familiar with. I can't honestly say one way or the other whether or not I would like it if it weren't attatched to this video. Maybe, maybe not.
http://www.youtube.com/watch?v=sWZWZP0KrnE

Tenacious D - "Wonder Boy" - Anime Music Video
What's odd about this addition into my little rant is that this is NOT the actual video for the song... this is a masterfully edited series of clips from the endlessly brilliant Japanese anime 'FLCL' put to an equally brilliant Tenacious D tune.
The reason I include this is to point out that editing, like anything else, CAN be an artform when the editor has a vision.
http://www.youtube.com/watch?v=XFmNNRIdbCE

Peter Gabriel - "Sledge Hammer"
What can I possibly say about this video that hasn't been said a million times already and a million times better? It's art. It's sheer brilliance. SO far ahead of it's time. While everyone else was making videos that were basically just taped concert performances or gyrating bikini girls trying not to laugh at David Lee Roth, Peter Gabriel made THIS. Peter Gabriel is the greatest musical genius of the modern age. Period. If you disagree, you are utterly and pathetically wrong.
http://www.youtube.com/watch?v=NaPYQysTHtA