Anyone with a programming background would love to take a shot at becoming a video game programmer. It's a really tough job to get, especially at a big studio such as Valve, Microsoft, EA, or Activision for example.
But there are some very good tricks and tips to be able to wow any developer at an interview, and if you follow with me, I'll show you the easiest way to get any Video game programmer job you want!
Firstly you have to ask yourself "would EA want to hire me?" Drop all the fantasy of "If I worked for (company x), I would do (feature y) so much better" and actually look at your talents.
What Can You Do?
Can you build a Concentration (memory) game? A Tic-tac-toe game where the AI always wins? A Minesweeper clone? Snake? Tetris? What about a Sokoban styled puzzle (box pushing puzzle)?
If you can't build all of those, there is a cold hard truth you are going to have to realise. No AAA developer is going to hire you, period. Feel free to put these things into your resume, along with a piece of programming that shows precisely how talented you are.
Alternatively one of the best ways to get a video game programmer job is to take the backdoor route. This route gets you into the AAA companies with a minimum of fuss and hassle, and gives you a platform to show them precisely what you are made of.
While this route I haven't personally done, my uncle did it and is now the lead programmer very high up in Sony earning way over 100,000 a year. If he can do it, you can too if you have the skills and the ability to do the job and of course the will to want to get out of your chair and step up to the task.