How many licks does it take to get to the center of a Tootsie Pop?

That is an interesting question.  Unfortunately there are too many variables involved to get a definitive answer.  

One variable is the size of the Tootsie Pop.  I'm sure the Tootsie Pop company has a set margin of error for what is and is not an acceptable sized sucker; however, there is always going to be some variation in exactly how much hard candy coating is covering the inner chocolate.  

Another variable is the size of the Tootsie in the middle.  A slightly larger Tootsie would result in a slightly thinner candy coating in order to have the same standard sized pop.  A thinner coat would require fewer licks.  

The duration and intensity of a lick are also variables that would have to be accounted for.  If a person left it in their mouth the entire time, does that count as one lick?  If a lick is defined as what the tongue touches while outside of the mouth, then tongue length would need to be standardized or accounted for.  A longer length tongue has the potential to get to the center with fewer licks, because it spends more time in contact with the candy coating.  Tongue pressure on candy is another variable.  The friction between the candy and tongue is going to be inversely proportional to the number of licks.  More friction, fewer licks. 

You could account for all of these variables by setting up a variety of controls and using a large sample pool of people.  Personally, I would rather just eat the candy and continue to wonder how many licks it really takes.  

If that's not good enough for you, Purdue and the University of Michigan have both done studies to answer your question.  Both studies used licking machines in order to reduce the number of variables, but both studies arrived at different answers.  I've linked them below.