Warcraft 3 is definitely what got me into programming. Namely the map creation, kudos to Blizzard for that.
Warcraft 3 is probably the game I have played the most in my entire life, hours wise. I started in Middle School, and the custom maps completely blew me away, providing countless of hours of entertainment. A friend of mine was really into making maps, and I asked if I could help, he pointed me to a scripting guide, and the rest is history.
But definitely, games can be a driving force for getting started with programming. Especially games with extensions/addons/plugins support. I also have an acquaintance that got into programming by making Addons for World of Warcraft.