One low-tech but effective solution, suggested by Mike (Mr. K as he's known to students) is to design an editable username/password table in Excel spreadsheet which can then be e-mailed to the entire staff. The form will come be pre-filled with our school's most commonly used applications and website addresses leaving the username/password column blank. Teachers can simply input their own unique username/password in the appropriate row, save the file on their computer desktop or print it out. They can tape this under their laptop or stick it in a file in their desk. It's kind of like having our own personal phonebook for our username/passwords.
One word of caution: This solution is not recommended for critical data such as online banking, Amazon, or other sensitive information.