I consider the minimum playable FPS for my games to be: 25.
From watching various benchmarking apps (especially the Crysis built-in ones) anything below this is noticeably choppy. You'd want this to be the absolute minimum though, not an average.
I consider the maximum FPS that I can perceive to be happening: ~90.
Just guessing at this but I can definitely spot the difference between a 60Hz refresh on a CRT monitor and a 85Hz refresh. Try this at home: Stare at an object placed just to the side of your monitor and allow your eye to notice the monitor in your peripheral vision. Try it at 60Hz and 85 Hz and see if you notice a difference in flickering.
I consider the 'limit' the eye can see to be around 30FPS: no
I consider the 'limit' the eye can see to be around 60FPS: no
I consider the 'limit' the eye can see to be higher than 60FPS: yes