My favs, no particular order:
Beyonce: Single Ladies
Everything with Weird Al Yankovic, even the fan videos
Pussycat Dolls: Jai Ho (although you need to watch Slumdog Millionaire to catch the references)
Afroman: Because I got high
Alien Ant Farm: Smooth Criminal
Blind Melon: No Rain (Acoustic on MTV’s Unplugged)
Eminem: Without Me
Pretty much everything by the Foo Fighters
Lonely Island: Jizz in my Pants
Ok Go: Here it goes again
Paula Abdul: Rush Rush
Queen: Bohemian Rhapsody
Run DMC: Walk this Way
Weezer: Buddy Holly
El Debarge: Who’s Johnny
Seven Nation Army by The White Stripes is an awesome video, not to mention song.
Saved by Zug Izland also has an awesome video. Watch it and you’ll see what I mean for sure. 
What’s a Girl To Do by Bat For Lashes was introduced to me a long time ago by exactly one of these types of threads.
I feel it should also be noted that none of these fucking videos are playing for me right now. As documented in The Pit recently, YouTube is being a huge bitch to me right now for reasons unknown.
Double post because my internet connection sucks large equine testicles.
•Pretty much any of the videos from Madonna’s Ray of Light.
•Pearl Jam’s Do the Evolution.
•Vangelis’ Conquest of Paradise. (This one is probably cheating)
•I have to admit a fondness for George Michael’s Freedom 90.
•…and Sad Kermit’s Hurt, for whatever that counts as.
Huh. Woulda thought this one’d get more responses, myself.
What the hell—a couple of more, for the road:
•Special by Garbage.
I’m a sucker for air combat.
•Here With Me by Dido.
'Cause I’m a big softie.
•Hide and Seek by Imogen Heap.
Probably too trendy, I know. Bah, I like it anyway.
•Aaaand…what the hell, Love Song for a Vampire by Annie Lennox.
Because Annie Lennox is very cool and spooky.
I don’t think I will ever tire of Virtual Insanity by Jamiroquai.
Björk’s video for All is Full of Love is something special.