Millions of people now have Paypal accounts, online access to bank accounts, and other online access to financial transactions, typically protected only by the passwords they pick themselves.
If you are still using your dog's name or some other simple four or five letter word for your password, you may want to read this short article on the various ways bad people are using to steal passwords.
The best passwords are at least eight characters long, and consist of an apparently random string of mixed case characters and at least one digit. My bank also requires a special character (like an ampersand or a dollar sign).
If you pick four or five good passwords and use them consistently, you can protect yourself and still not go crazy trying to remember them. For example, use one or two passwords on all your insecure sites (e.g. news sites, etc.) and don't ever mix the passwords you use for financial sites.