I get gaming sickness all the time. Almost all games in First-Person, and certain games in third person (like if you're right up to the back of the character, or the screen bounces while you run, or the bg moves constantly.) I've almost got what makes me sick in games down to a freaking science. First time I felt motion sickness while gaming was with Duke Nukem.
To fight it, I've found a few steps that can help:
1. Always play in a well-lit room. If you're playing at night, have some lights on.
2. Take breaks after every 30 minutes. Lets the eyes rest.
3. Don't sit insanely close to the screen. Obvious reasons.
4. Take Ginger Pills (or Dramamine) before playing games that you know will make you dizzy. Ginger pills are easier to come by and don't make you drowsy.
5. If you do feel sick, don't push it. Pause the game and take an insta-break. During this time, step outside for air or drink a glass of water. Chew gum. Pet a cat. Something to get your mind in the right order.
I still can't play certain games (most FPS's), usually do to the game's mechanics - such as a shoddy camera scheme. And I also found that Wii games don't make me nearly as sick as other systems. Something about sitting forward with a wiimote opposed to a standard controller. Even gamecube games on the Wii can make me sick, but I can somehow complete the Metroid Prime series and Zelda Twilight with a wiimote with little to no problem.