That is the title of an awesome Bob Marley tune:

http://www.youtube.com/watch?v=jGqrvn3q1oo

He is saying "don't cry my woman".  The song is a reflection on their past together as he prepares to be away from her for a time.  (At least, that's how I understand it.)

This should be the words from a man, I think. He must have been hurt by a woman. So, it means 'if I never fell in love with her, I would not feel so sad now.'

(No Woman,No Cry)is one of Bob Marley's top songs,no cry equals do not cry(Jamaican accent).other than that I'm not aware of other use of the sentence.

Don't fall inlove with a woman... she will make you cry haha lol..

It means (My woman, don't you ever cry.)