The number of possible cell divisions is limited by the length of the Telomeres, but they have not been studied enough at this point to make any universal conclusions:
http://en.wikipedia.org/wiki/Telomere
"The phenomenon of limited cellular division was first observed by Leonard Hayflick. Significant discoveries were made by the team led by Professor Elizabeth Blackburn at the University of California - San Francisco. In 1998, Geron Corp. developed techniques for extending telomeres, and demonstrated that this prevented cellular senescence.
Advocates of human life extension promote the idea of lengthening the telomeres in certain cells through temporary activation of telomerase (by drugs), or possibly permanently by gene therapy. They reason that this would extend human life. So far these ideas have not been proven in humans."