Caution: increase of the number of phishing e-mails addressed to AdWords users

These past few days, AdWords users have been flooded with phishing e-mails concerning Google Adwords. In these e-mails, users are asked to send their password, to accept new conditions of use, to re-enter their credit card information, etc. The e-mails seem to come from adwords-noreply@google.com, but the answers are sent to the frauds.
Google advises never to answer e-mails that ask for personal, financial or account information and to check the message headers in case of doubt.