Microsoft's advice on Strong passwords: How to create and use them recommends "Do not type passwords on computers that you do not control. Computers such as those in Internet cafes, computer labs, shared systems, kiosk systems, conferences, and airport lounges should be considered unsafe for any personal use other than anonymous Internet browsing. Do not use these computers to check online e-mail, chat rooms, bank balances, business mail, or any other account that requires a user name and password. Criminals can purchase keystroke logging devices for very little money and they take only a few moments to install. These devices let malicious users harvest all the information typed on a computer from across the Internet - your passwords and pass phrases are worth as much as the information that they protect."
Sound advice. You need to balance the convenience of web access whilst waiting for your coffee, plane or train, against the inconvenience of having your identity stolen and your bank accounts cleaned out.
More links on keeping secrets