It was the 1970s Hobbit animated film that did it for me. I loved it, and its fantasy world was forever burned into my young brain.
A few years later, when I was in the third grade, my parents gave me Milton Bradley's Dark Tower for Christmas. It was the best thing ever. I devoured the rulebook. The game's play, story, artwork, and components melded perfectly with Tolkien's world. The neighborhood kids and I played it endlessly for years.
My geek-ness was certified in junior high when the same neighborhood kids and I got hooked on Advanced Dungeons & Dragons for a couple years. Loved it. Books of monsters, fantasy worlds, character stats. Wow!
In parallel, I've always been a huge space opera fan -- Star Wars, Star Blazers, Robotech/Macross, Battlestar Galactica ... some Star Trek. But I've yet to play a space-theme game as engrossing as Dark Tower and D&D was in my youth. (Although, if I found the right group and had the time, Twilight Imperium sure looks fun!) [UPDATE: GMT's Space Empires 4X is shaping up to be *that* game.]
So I'm mostly a fantasy- and space-theme fiend, with a tendency toward con-sims. I'm also primarily a solitaire player, due to family, career, and home-business time constraints. My game ratings are based almost entirely on solo play.
If I play historical wargames, it's mostly due to their solo-ability and out of intellectual/logical curiosity. (I'm a military-history nerd, and yes, sometimes read wargame manuals for enjoyment.) It's a taste I probably acquired from playing the 80s Napoleonic version of Risk over long summers as a kid.
Ultimately, boardgaming scratches a broad swath of my itches -- including art & design, and even hand-crafting. I have some games simply because they're beautiful to look at. Some games I have strictly for painting or for crafting.
Love it all.