What happened to Twitter can happen at any company. The attacker exploited common problems in many corporate networks.
First, there was the problem that Twitter’s server had a password set to “password.” Executives would find news of their own server passwords being so weak as inexcusable! Then, there was another breach that was caused by several user blunders including using the same password at both gmail and hotmail.
Do any of your users, or you, use the same password at more than one site? Change them. Get a password manager such as RoboForm or MyPasswordManager. A password manager remembers all your passwords for you – all you need to remember is your password to the password manager. Not perfect security, but a whole lot more secure than using the same password at more than one site! Protect yourself.