The answer above is misleading on many levels. To be sure he met the wrong women, but the reason his lost his power was not on account of this. 

If we look at the story of Samson, we will realize that Samson's birth was miraculous. His mother was barren and was not able to have children, but God was gracious. He promised to her that she will bear a son, but that she would have to dedicate him to the Lord. Here are the words of Judges 13:2-5.

A certain man of Zorah, named Manoah, from the clan of the Danites,had a wife who was childless, unable to give birth. The angel of theLord appeared to her and said, “You are barren and childless, but you are going to become pregnant and give birth to a son.Now see to it that you drink no wine or other fermented drink and that you do not eat anything unclean. You will become pregnant and have a son whose head is never to be touched by a razor because the boy is to be a Nazirite, dedicated to God from the womb.

The quote is lengthy, but it shows us that Samson was supposed to be dedicated to the Lord. It was called a Nazirite vow. Usually these vows were for a short period of time, but for Samson it was supposed to be lifelong. So, when his hair was cut, he disobeyed God. This is why he lost his power. Disobedience or the breaking of a vow to God is the reason.

The story of how Samson lost his strength can be found in Judges, Chapter 16.  Basically, he lost his strength because he trusted the wrong woman.  Samson fell in love with Delilah.  She took money from the Philistines to betray him.  She nagged him until he finally told her that his strength would be lost if his head were shaved.  Delilah then told the Philistines and had someone come and shave Samson's head. This robbed him of his powers.  In this way, Samson lost his powers by giving away his secret to someone who was only pretending to love him.