If you get email allegedly from Microsoft saying that your mailbox is full, it must be true, right?
The current version of this scam includes a link to a Google Docs form to make it easy for the scammer to harvest your account information. If you submit the information the form asks for, you will have enabled to scammer to log in to your account and either steal it or use it to spoof your account to send out further scam email messages.
See a message like this one?
Just delete it. Do not follow the link. Do not complete the Google Form.