"When you notice a fee increase, that should be an immediate alert to start shopping around and check the marketplace," said Richard Barrington, banking analyst for MoneyRates.com. "Don't assume the same things are going on everywhere."
But when shopping around, remember that a great yield and zero fees don't always come hand in hand, so you first have to figure out what is more important to you.
If you have a large amount of money to deposit -- say, over $10,000 -- you should typically look for a bank with a high interest rate rather than focus on the monthly fees, Barrington recommended.
That's because the interest you make would likely offset the fees.
But if you're just starting to save and don't have a lot of money to put into an account, you should find a bank that offers free checking -- which all eight of these banks have.
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Last updated January 28 2011: 2:44 PM ET