So you've created a strong password system following the tips outlined in Passwords: Creating and Maintaining a Strong Password System. Now you need to keep those passwords safe.
Don't leave your passwords lying around. Lock them up in a safe box, file cabinet, or other secure storage device. You can even maintain them in a an encrypted (password-protected) file on your computer. But don't write them on a sticky note and 'hide' it under your keyboard or stuck underneath the desk.
Don't reveal your passwords to others. If someone absolutely must have access to your account, change the password before you grant them access, then change it again after their access is no longer required.
Never give your password out in an email. Likewise, if you forget your password and have to request it be sent to you via email, change your password as soon as you receive it.
Don't use the default password assigned to you unless it's a hard requirement. Some ISPs, for example, pre-configure the account with a username and password combination. You might not be able to change the username, but you definitely should be able to change the password.
Change reset passwords. You might encounter a situation where you're locked out of your account and can't remember the email address you registered it under. If that happens, a phone call to the provider might be in order. After establishing that you really are who you say they are, they should be able to reset your password. As soon as the password reset takes effect and you are able to login again, change the password.
Gamers: don't give your password out in game. Never, ever give your password out to someone in game claiming to be a staff member (gm). This is rule #1 for all games - no staff member (gm) will ever ask for your email. Period. No exceptions.
Never, ever respond to an email asking for your password. Most especially, never, ever follow a link in an email pointing to a site which requires a login. Period. No exceptions. These email are called phishing scams and are extremely common. If you really feel there's a chance the email might be legitimate, go to the website via the traditional means - either by using a previously saved bookmark or by typing in the site address you normally use to visit the site. Do not type in the link provided in the email.
Don't use computers at Internet cafes or in hotel business centers to access any site requiring a login. Period. No exceptions. Internet cafes and hotel businesses are rife with adware, spyware, keyloggers and assorted other malware which likely will not be visible to the naked eye.