The question has so many variables there is no actual answer as to how many FPS can we notice, but here are a few things I've learned over the years:
1) 24 FPS is about when video can appear smooth
2) It takes more FPS for a game to appear smooth due to a lack of motion blur
3) We can notice a difference FAR beyond 24 FPS
4) Much of the difference between 60 FPS and 120 FPS is in how responsive the game feels with a mouse
5) Motion blur, due to pixel response and persistence, can prevent us from seeing a clear difference beyond 60 FPS
6) But with Lightboost, CRT's and other motion blur and persistence reductions, 120 FPS becomes much better visually
7) The more the scene changes, the more noticeable high FPS are. Panning your view makes 30 FPS look horrible, even with motion blur on a movie
8) Movies get away with such low FPS by being careful not to pan the camera view by focusing on people in the center of the camera
9) Higher refresh rates reduces the length that tears are visible. They never go away without V-sync, but they are less noticeable.
There are many other realities that complicate things.
Yes, there is a big difference between 60 FPS and 120 FPS when gaming in 1st person view. The difference is also pretty noticeable when your screen is constantly panning the view, like in Diablo type games. In RTS type games, it would be hard to notice much of a difference. The biggest differences appear to be in how responsive games feel, more than how they look.
The only correct answer is that displays haven't got fast enough to outpace our eyes yet. Anyone that says 'hurr 30/60 is the highest the eye can see' is simply a moron and can be disproved with 20 seconds and a method of setting up FPS caps.