How many rolls does it take to get each die number to occur 1/6 of the time?

I think you might be asking "how many rolls of a die does it take for all 6 numbers to appear at least once?"
That is called an "occupancy problem" and I'll explain more about that if you reply to this answer.
I think after 13 rolls, the probability becomes greater than 50%.
Here is an explanation from Dr Math:
http://mathforum.org/library/drmath/view/56679.html