Depends. Final height is reached when the growth centers of your bones close and further linear growth cannot occur. This varies in most men from 16-20 and women from 15-17. A single x-ray of the wrist/hand can be assessed for open growth centers. When open, more growth is possible, if closed it is finished.
16-19. After your growth plates close you stop growing in height. This is typically somewhere between 15-17 years of age for girls and 17-19 years of age for boys.