5. Use strong passwords and don't reuse your bank password elsewhere.
"Remember that if you use the same password on multiple sites, then it's only as secure as the weakest site," Wang said.
Use two factor authentication if your bank offers it, such as confirmation numbers by text message to your phone, Wang said.
Levin said you should even have unusual answers to additional security questions.
"If they ask for your mother's maiden name, say 'superwoman,' or something outrageous that you would only know," Levin said.
Litan said another extreme but secure way to bank safely online is to use a locked-down browser, a CD-drive that is "read-only" or have a dedicated computer solely for online banking.
6. Be active in monitoring your financial accounts.
Levin said he does not believe eliminating your online accounts is the answer because they can be the best tools to monitor your financial activity in real time. He suggests you monitor your online accounts at least once a day.
"Some people say that's an outrageous use of your time, but think about how long you spend in email or your Facebook account, and think about how much time you want to protect the financial integrity of your life," Levin said.
While legislators are pushing for legislation to penalize institutions that expose customer information through data breaches, Andrew Hoog said it may take years for laws to pass. And it is unclear how rigorously they may be enforced.
"If regulation was designed properly, that would be wonderful," Hoog said. "But it would be far better if the consumer demanded it. Businesses may listen if consumers said, 'We're going to leave your bank and find someone else because there are other banks that are more secure.'"