Look, I've been stalked.
The best way to deal is to break things off as firmly as possible, and to make whatever changes you need to in order that private numbers, etc. can no longer be found out. I'm going to address this next part as if it were you being stalked, but you understand it's on behalf of your girlfriend, right?!
That may mean: Changing phones. And phone numbers.
Letting friends, family and others know that this person is not welcome to make contact and that your private details are not to be given out.
Changing facebook and other social sites' userprofiles, and heavily editing private information on such sites.
Blocking offending people on facebook, MSN, email and other networks. If this does not work, then creating new, private accounts may help.
Changing postal addresses, and if the offender is persistent, residential addresses too. Though, if this is such a problem, you should be able to get a restraining order.
And finally, communication with those you trust. Don't isolate yourself. The more people know you are being treated wrongly, and what to do to help, the more likely you are to cope. Often, stalkers want you to be isolated, so they have control over who you see, what you do, and what you feel. Don't allow them to do that!
And finally, if your girlfriend has not told her stalker firmly before that he is not welcome, the next time he contacts her, it's time to tell him so. If she cannot do that, maybe it's something you can do as her friend and support.
That's all I can think of to help. My situation was resolved without the intervention of authorities, so it can be done. It might sound hard, but a life without harassment is worth it in the end.
And good on you for caring about your girl!