KeePass Password Safe can store your user name and passwords for any website including Web based email, Internet banking etc. Instead of remembering all your credentials just remember the KeePass Master password.
You can add a new entry in KeePass by selecting the category in left pane and right-clicking into the right pane. Fill in the information including the URL so that you can later right-click the entry, and then select URL(s) --> Open in Browser.
Under the Tools menu you find a useful password generator, a TAN wizard and the Options menu. There, I recommend you check the security tab’s first option and set Lock workspace after the following number of seconds to 60 or any other value you find secure.
Best practice: I consider KeePass the number one tool for account information which needs to be kept highly secure (However, for the vast majority of my web accounts, like logins to forums for example, I use a quicker tool called Roboform Pro).