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According to the official Tootsie Roll website, Tootsie Roll Industries has received over 50,000 letters from children claiming to have solved the riddle since the commercial first aired in 1970. The typical range of responses is between 100 and 5,800.

Tootsie Roll Industries notes that they are aware of 3 separate and completely unrelated studies which attempted to finally put to rest the ever eternal question of "How many licks does it take to get to the Tootsie Roll center of a Tootsie Pop?":

A handful of engineering students at Purdue University appear to have conducted the most research. They devised a "licking machine," with which they recorded an average of 364 licks to get to that Tootsie Roll center we all know and love. Their research also included having 20 human volunteers carry out the experiment as well. The results from the volunteers concluded that it took an average of 252 licks to reach the center.
One doctorate student at the University of Michigan created his own licking machine and came up with an average of 411 licks to reach the center of the Tootsie Pop.
Students at Swathmore High School conducted their own human-based experiment, resulting in an average of 144 licks.
If one were to take the average of the above averages, the result is an astonishing 292.75. This number seems unusually low, but when one takes into consideration how each independent study may have defined a "lick," it becomes apparent that the world may indeed never know.