Funny I was asking myself the same question a few days back. I think society is changing and there are less and less trustworthy friends everyday. But that is life, and since it is imposible for us to change all people, we should atleast try help and change our own.
So, I think what you should do, is to confront your friend, tell him/her of how hurting it is to see them break your trust. But, give a chance for an apology and for your friend to make it up for you. If it happened again, keep distance and try to show him/her of what they will lose by breaking your trust. But, if neither worked then its time to start looking for a new friend because some people are indeed not worthy if the trust we give!