The first thing I ever played was Cyan's PC classic Myst. The mysterious story, the beautiful enviroments, the richly detailed background, I completely fell in love with it from the moment I started. I had barely even heard of gaming so the idea of actually being able to explore a world, and even (In its own limited fashion) interact with the storyline was a revolution for me. It's probably influenced the way I look at every other thing I play.
First shooter was Retro's also brilliant Metroid Prime (Yeah, I know. I took me a while to expand into the rest of gaming).
First RPG was Bethesda's Oblivion. Ah, such fond memories of hours wasted walking from place to place instead of fast-traveling. First game I started modding too.