Gmail's Terms of Use do state in Section 3 that:

"You shall not, shall not agree to, and shall not authorize or encourage any third party to: (i) use the Service to upload, transmit or otherwise distribute any content that is unlawful, defamatory, harassing, abusive, fraudulent, obscene, contains viruses, or is otherwise objectionable as reasonably determined by Google."
 

First, if you feel that you are in danger, we suggest contacting your local authorities. For nuisance emails, we suggest setting up a filter in Gmail to send mail from the sender directly to your trash. If you have a Gmail address, please read How do I set up filters? for instructions.

Because message headers and senders can be spoofed using a variety of means, we're unable to take action on any user without further verification. In accordance with state and federal law, it is Google's policy only to provide information about a specific Gmail user pursuant to a valid third party subpoena or other appropriate legal process.

We apologize for any inconvenience, and we're sorry that you're receiving such messages."

 
So are we saying that Google cannot do anything about this problem? If so, then a move away from Google will be necessary and compulsory!