It's really hard to have a discussion about UO without the urge to talk about how important it was to me (I've noticed I'm not the only one).
So rather than resist that urge... Ultima Online is directly responsible for me being a programmer. I was 13 when I got a copy of the game and an account thanks to my parents. It wasn't the first game I'd played where I'd wondered how it had been made but it was the first game I'd played where I couldn't even conceive of how it could possibly work. It was so different from anything else that I'd played before, including the first 8 Ultima games. Trying to figure that out led me towards programming in general and to SphereServer, the UO server emulator. The scripting system for SphereServer allowed me to change the game (for me and my friends only, but still) and really explore what's possible. By the time I was 16 I knew what I was doing for the rest of my life, even if it wasn't necessarily anything related to games.