In the late 80's, when I was 6-7 years old, I had ZX Spectrum. Back then, I've mostly played "action" games. Then, one day, a friend of the family brought me "Maniac Mansion". I don't remember did I've even finished the game (was too childish), but technically, this was my first adventure game.
I've got my first PC many years later (in 1997, I think). But the first PC adventure I've played is "Broken Sword: The Smoking Mirror". I've first played the demo version I've found on a CD-ROM supplied with one of the Croatian IT magazines, and was so thrilled that I just had to get my hands on the full version. And this is it - I'm hooked on adventure games ever since.