As long as the computer you are using is your personal computer, it is okay to let your internet browser (Firefox, Chrome, Safari, Internet Explorer) remember your login info for you. Most browsers now will ask you if you want to save the login info after you have entered it into the boxes on the login page and clicked the login button.
You can also get a program like RoboForm or LastPass - which can remember passwords for you and also generate very secure passwords for you.