My beginnings were very similar to Lechuck's: I read an article on the game in a gaming magazine Gambler, in 1994. I didn't have a PC back then and I was 14, so I kept reading alien races descriptions and tips on tactics and let my imagination run wild. I still remember how much I was easily placing UFO in the very top tier of games I'd like to play.
My first PC came three years later, in 1997, and it already had several games on its hard drive - one of them the first UFO! This has changed my life. I played as much as I could without infuriating my parents, I kept seeing those low fences and fields of cabbage whenever I closed my eyes. The game was just as awesome as is it looked on paper, and it just couldn't be better.
Obviously there are other games I love and which consumed so much of my time, for example Civilization: Call to Power, for which we made a humongous mod with Dioxine (the biggest in the world, many years of modding), UFO:Aftershock (the other best thing in tactical gaming, especially with ACM mod), some pinballs (what happened to the genre?), One Must Fall '97 and a few others. But with none of these titles I formed such a stable, continuous relationship, which continues until today and is unlikely to ever end.