The video game industry is a wide open field, complete with dozens of possible options for those that want to craft the next great video game. For those that are good with numbers, find themselves incredibly adept at picking out small details and more than anything like seeing how things work on a basic level, video game programming might be the job for you.
As a game programmer, you must remember that you are not a game designer. It's not your job to craft the how or what of the game. You are instead tasked with taking a set of specific instructions and making them come to life in your code. The video game industry is filled with roles, but the role of game programmer is probably the most important. You lay the foundation for the entire project.
Over the years the role of a game programmer has become more and more specific, changing from a catch all designer, programmer, artist role in the 1970s to a very specific job now. There are more than a dozen different positions you might hold as a game programmer, ranging from game physics to sound to graphics, and artificial intelligence. Every facet you can imagine in a video game has a specific engine operating it. As a game programmer your responsibility will likely be working directly with one of these engines to help complete a very specific portion of the game.
You should expect to spend a decent amount of time in school preparing for this job, learning multiple programming languages and getting your degree in Computer Science. There's a lot of math and you'd better have a keen eye for detail, but for those that do, video game programming is among the most interesting and exciting jobs you can get as a programmer.
The video game industry is as varied as any and you might find yourself in a series of different roles, working on different projects every six months or so. Once you've mastered the details of your craft, it's a matter of specializing and video game design. That means getting to know certain engines, programs and concepts.
For example, a simple role playing game might require a single physics engine programmer, a job that leaves you with a lot of responsibility and duties. Your next project might be a shooting game though, or an action RPG, the kinds of games that require massive teams of physics engine programmers, putting you on a very specific detail, like gun mechanics.
Or you could very well find yourself on an entirely different team, programming artificial intelligence for alien enemies. The possibilities are endless and the variance in the programming you'll do immense. But, if you find that you want more than anything to work in the video game industry but aren't a math wizard or want to get involved in the visual aspects of game design, there are still plenty of options open for you in the game industry.