Depending on your age... stopping it might be quite impossible if you've already done it. Only those with the greatest discipline and wisdom, like monks can really control themselves. It can come to a point where they discover there can be far more to life then orgasms and such, and would rather do other things that are more productive. In fact, they can lose the desire for sexual intercourse completely, which is what a lot of people associate as old age. Yes I can see that old age makes us flaccid and sagging and too tired, but a few elders that I have heard of realized that they don't need it in their lives at all whether or not they have the option, despite the fact that when they were young, they would discuss things like "Oh man, I never want to get old, I won't be able to party and have sex like I am now". They simply don't care for it anymore.
Eiri here has stated that masturbation is not damaging in any way, but I I'm not sure she is completely right (sorry =( ). She is right indeed about that it does have health benefits.
Masturbation or at least ejaculation through sex or something should be done if you want a healthy penis, yes. Underuse of your sexual organs can lead to prostrate cancer and such, but overuse can also lead to inflammation in the prostrate. Same goes for everything else in this world.
I can see that masturbating may be embarrassing, but I don't see how it clashes with ethics and morality? You are not cheating on somebody, you aren't giving away your virginity (if you still have it), etc, so.... what you mean???