Is there any law against harassment through the Internet?

I'm not talking about chatroom abuse, so and so called me ugly etc. I'm talking about e-mails, messages etc. from a person that is threatening and harassing you, and refuses to leave you alone. What happens if you block this person, yet they keep making new accounts to harass you with? Is there anything that can be done about it?
Yes, they do have my personal info. They had that first. That is how they found me on thet net.