I don't have a single card that got me hooked, but a couple of sets. The first cards I ever got were in packs from the '87 Topps set. The ol' wood cards.
My Dad brought me some packs of these (and the '88 Topps cards) from time to time trying to get me into liking baseball.
I really got into cards after my parents split up and my Dad and I would buy '89 Topps packs every time we were at a store that sold them. They were so easily accessible that I ended up with a lot of cards from that set. I don't have most of our original collection now, but have LOTS of cards from that set. They hold great memories for me.
I slowly branched out into collecting cards of other sports for the next dozen years before starting to focus on more specific goals.
I have to say that I now own or have owned several cards posted in this thread. I (almost obviously) have that '84 Ozzie OPC posted by rmpaq5. I also have the '84 Donruss Mattingly, '88 D'russ Grace, and '89 D'russ Matt Williams. I never had the '89 UD KGJr, but I have/had the Donruss RC and Fleer RC. I still have the Donruss RC, but it is in not-so-good shape, but I pulled it back in 1989 or 90 when I was a young teenager and didn't exactly now how to take care of my cards then.
I do love seeing the cards that folks are posting though. So PLZ keep them coming.
EDIT: I also had that '88 Schmidt. I might actually still have that one. The card I remember most from the '88 Topps set was the Mike Greenwell card. I can't remember if it was an All-Star card or an All Rookie Team card. Mine ended up with a crease across the bottom right corner, so I probably still have that one too.