But she also made one where she did appear.
Some of the Alan Parsons Project’s videos, like Don’t Answer Me.
Backwards eating Asian kid is the only person in the video From Your Mouth by God Lives Underwater.
Also, in the 80’s Herb Alpert and Janet Jackson did a duet called Diamonds in which Alpert appears, but not Jackson.
It was actually more a shot of the speaker than anything. “Bastards Of Young”. I thought it was the best video ever when it came out. Unfortunately, it’s not on Youtube, but I did find it here.
Most of R.E.M.'s videos from the IRS years (excluding “Can’t Get There From Here”) didn’t feature the band, notably Fall On Me and It’s The End of the World As We Know It (And I Feel Fine).
That Lego White Stripes video is pretty awesome. The Spitting Image Genesis was nightmare fuel.
This one maybe barely counts - another David Bowie movie theme: When the Wind Blows
There’s obviously some hand-drawn Bowie in different styles and possibly rotoscoping. I don’t think there’s any live-action Bowie footage or still photos included, but I can’t be certain. I also never saw this aired on American TV or included in any of his video collections, but it apparently aired on Japanese TV.
Pearl Jam hasn’t appeared in any of their videos since Jeremy.
I don’t remember the whole video, but I don’t believe Def Leppard appear in the video for “Women”, do they?
Equally hazy is my memory of Tom Petty’s “Running Down a Dream”…wasn’t that whole thing animated? I remember parts of it but I can’t remember if there’s any live parts.
Nope, all animated.
The Pet Shop Boys are absent from their “Numb” video aside from a “blink and you miss it” still photo inside a wavy snowglobe at the end.
http://video.google.com/videoplay?docid=-3750369423004056118#
(It’s worth a look for its “Homer Simpson’s Expensive Mr. Plow Commerical”-ish WTF-ness. 
)
A live-action Tom Petty appears, opens a book, the first chord sounds, and the animation begins. He reappears at the very end to close the book: http://www.youtube.com/watch?v=wKo6oU3Jk4c
Oh yeah, I completely forgot about it, and it’s one of my favorite videos.
Melissa Etheridge’s Come to my Window does not feature the singer, only Juliette Lewis
Actually it does.
Yup, they’re in it!
They appear in a couple of them in near-total darkness. You can’t really see what’s going on beyond “guys with guitars”.
The video for Pearl Jam’s Do The Evolution is one big creepy cartoon which does not feature the band.
The video for U2’s Hold Me, Thrill Me, Kiss Me, Kill Me does show the band, but only as hand-drawn animations. Does that count?
Prodigy/The Prodigy have a bunch of no-band-member-appearance videos in addition to Smack My Bitch Up, they’re not in Voodoo People, for one.
If there’s a genre where you won’t see a no-band-appearance video, it’s heavy metal. I’ve been racking my brains and I can’t think of a single one.
Massive Attack’s Teardrop is just one long creepy shot of an infant in the womb.
I haven’t seen it yet, but supposedly the band will be in the The Fixer video from their new (great but way too short) album. TECHNICALLY the band wasn’t in the Life Wasted video, but molds of their faces were made and then animated with stop motion.
Damn, I was gonna mention R.E.M. They also don’t appear in “Orange Crush” and “I’ll Take the Rain.”
I’m fairly sure that Blur didn’t appear in any videos for their last album (of original material), Think Tank.
Michael Jackson isn’t in the video for “Man in the Mirror.”
New Order might own this category. They don’t appear in the following videos (in addition to the aforementioned “Crystal”
“Fine Time”
“Round and Round”
“Waiting for the Siren’s Call”
“Krafty”
Trivia question - anybody remember the name of the fake band that appears in the “Crystal” video?
The Smiths don’t appear in the video for “The Queen is Dead.”
U2 didn’t appear in one of the videos for “One” (the buffalo one).
Theere is, on the other hand, the video for Paranoid Android. All hand-drawn, nary a sight (did I use that expression correctly?) of any Radiohead member.
Actually, the band (drawn) is in the video. They’re in the background during the bar scene.
Dreams, Van Halen
25 or 6 to 4, Chicago