The most important rule of password use, especially when used for online logins, is to avoid reusing passwords. From there, one’s method of keeping track of multiple passwords can vary considerably. While memorization is an option in theory, in practice a lot of people make use of a password manager like Lastpass or KeePass. For those with increased security concerns, though, you may want to implement a USB password keeper like this one based on an ATtiny.
An interesting link found among my daily reading