Eliane,
I once had a boyfriend who had the same issue with his ex. It seemed likw she had no life of her own -- all her time was dedicated to "break" his life and make it as miserable as possible. She was spreading all kinds of rumors, was calling both him and me at least once a day, and even turned my friends against him. I suffered from all possible kinds of abuse; she even got that far to call my boss at work
and asked whether he's not concerned that one of his employees (me) is dating a drug dealer... (luckily, my boss was a wise person and this caused no harm).
What we did with her was what is actually suggested by other people here -- we tried to ignore her as much as possible and lived our lives. It wasn't too effective -- it took 1,5 years for her to get lost
- although you could say, eventually it worked anyway. Still I must add, I really loved that guy back then and was surprised myself that I did not get tired of this and did not leave thim (though we still parted later on) -- it takes tremendous efforts to deal with such issues...
Anyhow, there might be other ways out that could be considered before turning on the "ignore" button. In the civilized world, your ex-bf's actions are in many cases a subject to the law. You could always report him to the police, or in case of physical abuse -- even get the court to issue a decision which would oblige your ex to stay away from you in a specified distance (and he would also have no legal right to contact you in other ways).
In less civilized world, common issues are solved by hiring a muscular guy to do some "man talk" -- which is not something I would recommend, but generally it might be good for you to have someone standing by you -- firstly because of the psychological support, and secondly -- a devoted person's company would be helpful when you're going out (I don't mean that this person should kick all the devils out of your ex -- I think his company might help you to feel more secure).
I wouldn't very much recommend moving to another location though... First of all, there is no guarantee he will not be crazy enough to follow you if he finds out where you moved to, and it is very likely that sooner or later he will find out. Secundly, he is not worth that sacrifice, that you ran away and built your life from scratch... Finally, I'd think it's way better to have this problem solved once and for good, so that there was no threat of your ex appearing in your life again someday in the future.
And make sure you don't enter the game that he started, i.e. don't try to revenge or even demonstrate stronger reactions to his creapy acts. This would only fire up his enthusiasm.
Lastly, gather all your strengths for the timebeing. This is hard situation, but sooner or later you will refer to it in the past tense. Try to think of it as of hangover from a bad relationship (I know this does not soothe very much now, but still the fact is, it could have been worse -- you might have married the bastard and might be having to deal with even worse issues now). Try to think of the positive things you'll do once this problem is solved. Get support from people around you, make sure to have someone close to you whom you could turn to in case you need help or maybe just to talk to.
Best of luck to you, and congratulations on making a huge right decision in your life!