The Red hot Chili Peppers' Blood Sugar Sex Magik is the first cassette tape I can remember purchasing with my own cash. I listened to that tape so many times that I wore it out.
I also had such classics as Poison's Open Up and Say... Ahh! My older brother had / has a copy of the original cover art, but I was a bit too young to really grasp what the controversy was about.
I also had Van Halen's OU812, Guns n Roses' Sweet Child o Mine single, and at least one Whitesnake album, but really those didn't get much air time.
However, Def Leppard's Hysteria was in heavy rotation during my early youth. Who can forget those jeans?