Games run at the highest frame rate your system is capable of, or the maximum refresh rate of your monitor. Whichever comes first.
As the previous poster said, 120Hz (a/k/a 3D) monitors are great for gaming, even in 2D if your computer is capable of supporting the higher frame rate for the games which you play. Even people who really enjoy the 3D most likely use it less than 50% of the time.
It is widely accepted that Nvidia Stereoscopic 3D is quite a bit ahead in terms of driver performance than AMD HD3D, so if you are adamant about 3D gaming, I would definitely recommend an Nvidia setup.
And remember, rendering two perspectives at once is the same thing as rendering twice the resolution in terms of what it requires to perform.