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60-120-240 Hz Television

Well, apparently enough such that those features make quite a difference. The brain doesn't have to process the whole image - just a small portion to notice stepping in the motion.
It actually differs from where in the field of view the source of flicker is located, and to the birgthness of both the output and the envroniment. Other factors may also have an effect, like the distance between the display and the viewer. It also varies from individual to individual.

Because of all this, there is no accurate answer to the question, and it can best be described as a multidimensional function including several variables (each containing some uncertanty) and bell-curves. In order to give an answer, the most extreme causes from each factor has to be calculated together in some way (and after all, that will theoretically only be for the extremely few people of the extreme cause).
It's not images per second, but amount of detail transmitted which is important. Double the images per second and you double the pixels transmitted to the user. Simply compare 16mm stills with 16mm movies and you will know what I mean. The stills are crappy but the movie is quite usable. Movies have amazing detail compared to stills. The effect works as long as the frame rate is high enough to avoid flicker - say 24fps or so.
It also depends on the technology used, my plasma at 60hz looks better than an LCD at 60hz, and i've put two tv's side by side and had several people say the same thing.

I always buy plasma (even though they get a little hotter) just because the picture is a lot better than any other flat screen technology i've ever used because i actually get true blacks, thus a much, much better contrast ratio.
The jump to 120 Hz was all about eliminating 3:2 pull-down when playing movies at broadcast frame rates (sat/cable/terrestrial) which the eye can definitely see and is very very distracting. The 240 leap had more to do with marketing and selling more TVs than visual improvement (though there was some).