Requesting old statements

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If you need to verify a charge or deposit, be prepared to fork over some money.

Bank of America customers must pay $3 to receive copies of checks, statements and deposit slips (but there's no fee for the first two check copies in some cases).

HSBC charges customers $5 for requesting a photocopy of a check or statement, while Capital One charges $3 per statement for credit card customers. Credit card customers at TD Bank must pay $7 to get copies of statements. Otherwise they can access them online at no cost.

"Staff have to spend time researching to find the old statements or documents which are archived after a certain period," said Feddis.

If you need something specific researched about your account history or want to dispute certain transactions, Bank of America charges you a research fee of $20 an hour. At Chase, this will cost you $25 an hour, while copies of statements cost $6.

Receiving money

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You're probably used to paying a fee when you need to wire money to someone else. But some banks even charge you to receive money.

Chase charges $15 for incoming wire transfers. You're charged the same amount for receiving money at PNC.

While banks say the fee helps cover the costs of providing a secure, reliable system, the charge can be avoided if you choose the right account.

"If you're an investor who frequently has wire transfers coming in or out, this is something that can really add up," said McBride. "Make sure you're aware of the fees before you sign up for an account, and pick one based on your habits."

Redeeming rewards points

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They're your rewards points. You've earned them. So now you can redeem them for a free ticket to Hawaii, right? Wrong.

American Express charges $0.0006 per point for domestic frequent flier point redemptions, with a maximum fee of $99. The charge offsets the federal excise tax American Express pays when these redemptions are processed, the credit card issuer said.

At Wells Fargo, you have to pay a $24 fee for each airline ticket issued through the bank's rewards vendor.

"That just defeats the whole purpose of the rewards in the first place," said McBride. "When signing up for rewards programs, you need to evaluate all the benefits relevant to the costs, and redemption costs clearly erode the benefits."

But for now, these redemption fees are the exception rather than the rule, so you can still find banks that won't charge you anything to cash in your points, said McBride.

Closing your account

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Sick of all the fees your bank is charging you? You can always close your account. But before you do, beware of another fee coming your way.

PNC and U.S. Bank charge customers $25 for closing their accounts within 180 days of opening them. Chase charges you $25 for shutting down an account within 90 days of becoming a customer.

Feddis said it costs banks about $20 to open a bank account, including the cost of determining that customers are who they say they are and that they can properly manage the account.

"It also supports the cost of the system which allows banks to provide secure, reliable, and convenient payment system which allows people to access their money 24/7 from anywhere in the world by check, debit card, online, etc.," said Feddis.