Your password is the key to your AOL account. If someone knows your password, they can use your account - and you'll end up paying for it. You wouldn't give the keys of your house to a stranger, would you? Protect your AOL password in the same way. It's as simple as this - Never EVER give your password to anyone!
For added security, you should also make your password hard to guess (combinations of letters and numbers are best) and change it regularly by signing-on to AOL and going to AOL Keyword: Password.