It's incredibly important to keep your email password secure. Many banks, online retailers and other web services will allow you to reset your password by sending a message to your email account. So, if someone guesses your email password, it's possible for them to gain access to many of your other accounts through it. How can you keep your email password secure?
Don't reuse passwords for your important accounts. A password is only as secure as the least secure site you use it on.
Make it hard to guess. Again, a password is only as secure as you make it, and if you use the password "password" (which a very surprising number of people do), it's not going to be that hard to guess. Use a mix of letters and numbers, and make it at least 8 characters.
Write it down. As I read somewhere once, "we've already developed a system for keeping important, private information secure. It's called a wallet."
Get help. Programs like 1Password, which generate random passwords, keeps track of stuff, and can auto-fill passwords across browsers, are really useful. Then, you only need to keep the password for 1Password very secure.
There are also lots of passwords you don't have to worry about. Unless you are worried about people masquerading as you, any passwords you need for message boards, photo sites or any sites where you don't have a credit card on record, re-using the same password is fine.