You don't necessarily need the latest smartphone, such as an Android, BlackBerry or iPhone, to take advantage of many aspects of mobile banking. If you own a cellphone with Internet capability, you're in business. But make sure that your cellphone package includes a data plan or you might be paying extra each time you access your banking information.

If you already are using online banking at home on your personal computer, you may be able to access that same service using your cellphone. Plug in the URL of your bank into your browser to get to the bank's website, much as you would do at home on your PC.

However, some banks don't allow access to their online banking services through a mobile device, so check with your bank first.

Even simple-feature cellphones, such as flip phones that have been around for years, can be used for text-message-based banking.

"Some text messaging services are amazingly interactive and allow you to get your balance, latest transaction and do bill payments," Bissell says.