UPDATE:
It turns out Sabre has been experiencing similar problems recently, too. The eServices section of the GDS also has a warning about emails being sent to agents with the same instructions - click a link, enter personal details etc.
As a result, Sabre says it is changing the format of some of its emails to customers:

"Due to the recent phishing activity, we are lessening the number of links that we’ll include in our emails to you, especially links to login pages. If you’re concerned about a possibly fraudulent link, we suggest you type in the website address yourself (rather than using a link)."
ORIGINAL:
Amadeus has written its travel agency customers to notify them of a so-called phishing email scam asking recipients to log in to their accounts using a bogus link.
The problem first arose earlier this month when a small number of agents received the email, using an Amadeus logo and supposedly from an official email address.
Phishing is a fairly widespread and well-known form of interent fraud (common with personal banking accounts) in which an email recipient is urged to enter their details into a bogus site, effectively giving the host confidential details from the user.
An Amadeus official says:

"Obviously this was not an email sent by Amadeus nor information or action we would request from our customers.
"Therefore, we wanted to be very proactive in communicating with our customers that they should always be aware of and not respond to any suspect emails asking for their Amadeus information. And to inform them to contact us if they had any questions or concerns."
Agents who clicked on the link were asked to enter their username, password and industry ID on the fake site.
Amadeus North America president and CEO, Scott Gutz, wrote to agents last week, with details of how they can protect themselves from so-called phishing activity.

Do not open e-mails, e-mail attachments or click on links provided in e-mails from unknown senders.Be vigilant and report any suspicious communications immediately to your Amadeus representative.Keep passwords secure. Avoid using weak passwords; use a combination of numbers, letters and signs, and change them regularly.Never reveal your Amadeus system credentials, such as your username or password, or any other confidential information, to third parties.If you feel you have been the victim of fraud, you should notify your local law enforcement agency immediately and inform your Amadeus sales or customer service representative.