Me too. The problem is always of technical nature, and, unfortunately, not all game developers are aware of the problem. When resolution, frame rate and FOV are just right, there is no motion sickness to speak of. That's why some games play perfectly fine while others give motion sickness. It all depends on your monitor, your GPU, your sitting position, and so on. Some games have good motion blur that helps (if the frame rate is consistent), while others have a horrible motion blur that would make me sick. So, tweaking all of those parameters, sometimes being forced to use external tools (like nVidia inspector) is the only way to go. With some games, even after all that tweaking, I still can't play comfortably. So it's a hit and miss. Third person games have the same problem albeit with much smaller nausea potential. Here's what you can do: try another monitor/TV, try different sitting position, try limiting the frame rate, try adjusting/hacking FOV, try turning on and off motion blur, aberrations and similar post processing options. Good luck!
If possible, always use an FOV of 90 degrees or more. I often find console ports that have too tight an FOV and no way to adjust it make me queasy (they're intended to be played from the couch). Another possibility is to make the crosshair bigger, or use a crosshair overlay - if you don't have something to "anchor" your perspective, it can cause nausea
I imagine this is a variety of car (motion) sickness. In that case, I wonder if diphenhydramine hydrochloride, which is used for exactly this, would be effective and help by giving you enough time in the game to get used to the pseudo-motion.
I do have the same issue that some FPS are just not playable for me, because of this. I'm still not sure what the reason is. I can play Battlefield 3 for hours, but some shooters make me sick after a few minutes. Maybe it is a mix of things, for example I always disable motion blur and shaky camera. Also, the FOV is often wrong when using a 21:9 aspect monitor.
Unless you have some medical problem, I think it just takes exposure.
Play until you are starting to get sick then stop. Overtime you will be able to play for longer.