It's still not clear at what framerate the human eye cannot tell the difference anymore. It is possible that humans can still tell the difference between 60 FPS and 120 FPS and possibly even beyond that. Keep in mind that humans are predatory carnivores, so our eyes are quite well developed for fast movement.
Anyway, the most important thing is that the screen has a high enough refresh rate. My screen, like most LCDs, has a refresh rate of 60Hz, so even if I was able to see the difference beyond that my screen wouldn't be able to display it. Anything beyond 60FPS is basically useless for me. If your screen has the same limitations don't even worry about framerate anymore, 60 FPS is the best you can see.
Most games have an upper limit for their physics simulation, like 60 FPS, and if the framerate exceeds it the graphics can be made independent. Then the game interpolates the position of an object. in other words, if a bullet is flying from A to B within one frame of simulation, the graphics will draw the bullet between those points, but the actual bullet will still "teleport" from A to B. This creates the smooth look, without breaking physics.