I think I read somewhere the minimum FPS the human eye can detect before things get noticeably choppy is 25 fps, personally I believe you can perceive finer or smoother framerates above that say 30-40. If you have a constant FPS above that range its wasted graphics power really.
This is a pretty common urban legend: in reality,
your eyes are not digital devices and therefore don't have a "refresh rate" or "FPS" (or, indeed, "frames"). Your eyes see all light that enters them continuously, and can in certain situations pick up
extremely subtle differences.
More important than your eyes for this, however, is your brain, and how it perceives motion. This is sometimes referred to erroneously as "persistence of vision" (which is a separate effect not as important for movies and games as was once believed). Basically, your brain is willing, under certain circumstances, to "fill in" the gaps between frames of a movie/game. The higher your framerate, the more likely your brain is to do this, but it also depends a lot on what it is (or thinks it is) seeing. So in some situations, you'd never be able to tell the difference between 30 and 60 FPS (or even lower; most movies are shot at 24 FPS IIRC), while in others you could have much higher FPS while still preventing your brain from seeing it seamlessly.
A good example of this is if you rotate the camera quickly in Oblivion - the greater the difference from one frame to the next (because you've spun that much), the more likely your brain is to see the two as separate images rather than movement from one to the next. In reality, I'm pretty sure you can spin fast enough in Oblivion that your brain will see the two as separate images even at extremely high (~200 FPS) framerates. Of course, the fact that Oblivion may also lag slightly when you spin suddenly as it has to paint a lot of new things it wasn't worrying about before also contributes to this. Various effects like motion blur can cause your brain to accept the same "motion" that it wouldn't before. Again, there is no hard number, it's all about what your brain thinks it's seeing.
An opposite example would be very slow movement - even at very low framerates, if the total movement from one frame to the next is low enough, your brain will see it as (very slow) movement. If a large-ish object - several hundred pixels - is moving at a rate of a single pixel per frame (or half a pixel using anti-aliasing, or whatever), you could have framerates as low as single digit FPS and still probably see it as seamless movement.