If you want to be a programmer, get your Computer Science or related degree... period. It will be the most helpful to you when applying, because it's their #1 required trait on all their job summaries. You're playing with fire if you take one of those "Videogame" degrees from an art school, because it will make it much tougher for you to get in the door.
You *could* get your start in QA, which requires little more than a high school diploma, but it will be next to impossible to move to any worthwhile position unless you have that piece of paper degree.

Senior Web Developer - Nokia