While I was walking with 'Abdullah (radiallaahu `anhu) he said, "We were in the company of the Prophet (sallallaahu `alayhi wasallam) and he said, 'He who can afford to marry should marry, because it will help him refrain from looking at other women, and save his private parts from looking at other women, and save his private parts from committing illegal sexual relation; and he who cannot afford to marry is advised to fast, as fasting will diminish his sexual power."
Sexual desire is something that has been created in man and it cannot be got rid of. Getting rid of it is not something that is required of the Muslim; rather what is required of him is to refrain from using it in haraam ways, and to use it in the ways that Allaah has permitted.
Halaal way: get married. If you can't, fast. It's going to help you resist the desire inshaAllah.
How to resist sexual desires? Read about the 2-step solution to this problem here.
Is there any benefit in resisting/breaking this desire? Read an interesting approach on this subject here.