The reason why Harry broke it is because, someone who wants to obtain it will have to murder the rightful owner to get it. It's a chain of blood and murder wherever the Elder Wand goes, and Harry broke it because it was in his procession. For someone to get it, they'll have to kill him, but if he died a natural death then the power of the Elder Wand would be broken. Even if someone recieved it after him, because they did not beat him in a duel with the Elder Wand.
So he broke it in vain to try and break the power of the Elder Wand, so they'll be less murders and deaths involved trying to get the wand.
And just think, it could have all been avoided had Harry not gone after Quirrelmort for no good reason.stare
Wouldn't you be a bit suspicious if someone's turban sneezed?
Well, yes. But there was no need for Harry to go after him, thereby endangering the Philosopher's Stone, putting his friends' lives in jeopardy, and freeing Voldemort's soul to wander around some more.
I despised that part of the movie. Why is it that the Elder wand is the one ancient magical artifact that is super easy to destroy?
While I loved the idea of Harry wishing to end the cycle of the Elder Wand, the fact that he could just snap it with his fingers and throw it off a cliff was ridiculous. The way it happened in the book made infinite more sense, not to mention he remembered to repair his old wand first like a non-tard