I study Genetics and Molecular Biology and have asked this question before to one of my lecturers. Evolution is the process by natural selection/survival of the fittest therefore every trait that has been passed down the generations, has done because it is an advantage.
Another HUGE aspect of evolution is time! In order to evolve as much as seen in X-men would just take millions of years if anything like that ever did happen. Another thing to think about is that a lot of the characters seen in X-men have super natural powers and therefore would never happen if you believe in science as science and supernatural do not mix.
Others aspects such as strength or increased intelligence may happen because it is an advantage and will increase your survival rates. This day in age because of medicine and other technological advances humans that may not have survived many years ago, survive therefore evolution is as at odd point.
To wrap it up, supernatural powers will never happen although increased intelligence, strength, quicker at healing themselves compared to other humans etc may happen.. Many many years away though... Millions maybe.