many people do not call the police now when they are threatened - not just anarchists. the protection the police (claim to) offer is pretty specific and extremely limited.
the fact that some people still don't think they have any other recourse has as much to do with the fact that police are seen to be the only legitimate users-of-force in this society, as it does with actually protecting ourselves. police, for a variety of reasons (not all of them even in their control), also tend to escalate conflicts rather than actually resolve anything.
one of the basics of anarchist thought is direct action, which means that we handle things ourselves. handling things can mean a wide variety of things, from violence to mediation (or all of the above), and could include various numbers of people (ie - who "us" is could be contextual).
also: what skitter said. ;)
edit: i did not answer the question that was asked in the headline because it has been asked directly (and alluded to) so many times. but once again (because this question is more direct than some others):
people would have to figure out for themselves and each other how they would want to address bad behavior, either before or after such behavior happened.
there would be some groups that value safety more, and there would be other groups that valued adventure more, and one hopes that there would be appropriate fluidity between such groups, since people change... and when there was disagreement, people would use a variety of tactics to figure it out, and some people wouldn't agree with the tactics, and probably some people wouldn't agree with the resolution, and NOT EVERYONE WOULD BE HAPPY.
anarchy is not a guarantee of happiness. anarchy is a way to allow us to do the best we can, which right now, we are actively (and on multiple levels) kept from attempting.