Have you ever seen an ABBA video?
Some of my favourites have been mentioned:
Take on Me
Gorillaz videos (Mostly 19-2000, though. Noodlez rocks.)
Don’t Come Around Here No More
Hey Ya
Some others…
Every Prozzak video from Strange Disease on (or was Sucks to be You first…? I’m pretty sure Strange Disease was the first, but either way, whichever of those was first, from that one on.)
Cradle of Filth - Her Ghost in the Fog and Born in a Burial Gown
Now a fairly random list of Japanese vids…
Mini Moni - Strawberry Pie, Mini Moni Telephone Ring Ring Ring and Jan Ken Pyon
Puchi Moni - Koi ni Knock Out
Malice Mizer - Beast of Blood
Tommy February6 - MaGic youR Eyes
Dir en Grey - Child Prey
Puffy - Boogy Woogie no 5 and Circuit no Musume
I like the Gorillaz videos, and also Californication, by Red Hot Chili Peppers.
I like one of Ludacris’s most recent videos, “Get back”, if only because the models there were different from the standard Hip-hop fare. And the special effects were good, too.
Radiohead - Street Spirit
Radiohead - High and Dry
Matthew Sweet - Girlfriend
Van Halen - Dreams (with the Blue Angels)
Wax - California (only video I’ve ever seen with a warning)
Bush - Machinehead
I’ll second Wicked Game and Fell in Love with a Girl.
D. Pirahna
Smooth Criminal- the Alien Ant Farm version…kid moonwalking down the street wearing a surgical mask…wtf?
Everlong- Foo Fighters…something about ‘Big Hand’ cracks me up every time.
Hero- Enrique Iglesias…no, I don’t know why.
Radiohead - Just.
Tony Powers - “Don’t Nobody Move (This is a Heist)”
An award winner in '83, pretty much only seen on “NightFlight,” and no longer available on VHS (never on DVD)
Mee too… 
Just about any of Weird Al’s videos.
Land of Confusion - Genesis
Money for Nothing - Dire Straits
Leave Me alone - Michael Jackson
Mystic Rythyms- Rush
Seconded.
Oh, and pre-1989 Duran Duran
If I told you that Smooth Criminal is originally a Michael Jackson song would that clear up the confusion?
“The Sound of Settling” by Death Cab for Cutie. It makes me smile every time I see it.
Hurt by Johnny Cash
Take On Me by Aha
Just about everything by Peter Gabriel, including “The Barry Williams Show”
“Sweet Dreams (Are Made Of This),” Eurythmics
“The Boys of Summer,” Don Henley
“Right Now,” Van Halen
“Land of Confusion,” Genesis
“Billie Jean,” Michael Jackson
“The Safety Dance,” Men Without Hats
“Mr. Roboto,” Styx
“We Didn’t Start the Fire,” Billy Joel
“Thriller,” Michael Jackson
“White Wedding,” Billy Idol
“Touch of Grey,” Grateful Dead
“Jeremy,” Pearl Jam
“Take On Me,” a-ha
“Hungry Like the Wolf,” Duran Duran
Most of Weird Al’s videos
“Money for Nothing,” Dire Straits
I’m sure many more will occur to me as soon as I send this, but that’s off the top of my head right now.