Michael Jackson's Moonwalker. Something about a robotic Michael Jackson just creeps me out. And yet, I continued playing. 
That's funny. I just posted this in the "Best non-classic games" thread:
I was overcome by the irony of "Michael Jackson's Moonwalker" when I played it this morning before heading to the office.
You are Michael Jackson, trying to collect small children as you make your way through streets beating up bad guys with a magical lazer that comes out of your finger and a special dance move that kills all bad guys on the screen. Also, if you collect Bubbles the monkey, you turn into Robo-Michael, and shoot more powerful lazers, all while a clunky version of "Smooth Criminal" babbles in the background.

A true non-classic classic.
A-he-he! Ow!