Especially when you plan on opening an online checking account, it is important to look for a bank that charges minimal or no customer fees. Many banks charge high fees on maintenance, which varies from one bank to another. Even if you do not get an account with zero charges, some banks also provide waiver services on monthly maintenance fees. Banks often offer such services to customers who make direct deposits or use a certain amount via their debit cards. If you find an account with that feature, you can enjoy monthly fee waivers on a regular basis.