This is the text of the message I received (once for each account, all created back around the same time January 2007):

  Hi, dewitt

  Twitter believes that your account may have been compromised by a website or service not associated with Twitter. We've reset your password to prevent others from accessing your account.

  You'll need to create a new password for your Twitter account. You can select a new password at this link: ***

  As always, you can also request a new password from our password-resend page: https://twitter.com/account/resend_password

  Please don't reuse your old password and be sure to choose a strong password (such as one with a combination of letters, numbers, and symbols).

  In general, be sure to:

  Always check that your browser's address bar is on a https://twitter.com website before entering your password. Phishing sites often look just like Twitter, so check the URL before entering your login information!
  Avoid using websites or services that promise to get you lots of followers. These sites have been known to send spam updates and damage user accounts.
  Review your approved connections on your Applications page at https://twitter.com/settings/applications. If you see any applications that you don't recognize, click the Revoke Access button.
  For more information, visit our help page for hacked or compromised accounts.

  The Twitter Team 

Best of luck to the security and support teams. Days like these are not fun at all.