A second ditto for Blotto's "Metalhead" and a-ha.  Here's a couple more that
haven't been mentioned.

Howard Jones - "You Know I Love You (Don't You)?" The next logical extension
of "Take On Me" in the animation department.
Kansas - "Fight Fire With Fire"  If only for the feverish nightmare scene
that coincided with the screaming break -  A pull-back shot of a needle in
the arm to reveal a giant mosquito.
Police - "Every Breath You Take" Its easy to forget what a welcome sedative
this was to the hyper-caffinated, jump-cut ridden video period in which it
arrived.
Police - "Wrapped Around Your Finger" another nicely slowed-down shoot.
Queen - "Bohemian Rhapsody" Seen on The Midnight Special with Wolfman Jack.
I didn't know what to expect from this band "Queen" but I knew that I loved
the song since I heard it on the radio a week or so earlier.  To be honest,
I expected to see a quartet of mustachioed Italians.  What I saw cemented
(warped?) my mind and made me the music/glam/Queen fan I remain to this day.
Golden Earring - "Twilight Zone"  The leather pants on the interrogating
women made a deep impression.  To this day I still don't know what the
lyrics are before the line "When the bullet hits the bone".

I'm sure I'm missing plenty.  My sister would kill me for not including
"Rio" or "White Wedding"

Mike