While most large nationwide banks offer mobile banking, don't assume small local banks don't.

"Smaller banks -- and even some credit unions -- have been agile and on top of this," Bissell says. Small banks are able to offer mobile banking by buying third-party services that host mobile banking applications.

If your bank doesn't offer mobile banking services -- and you don't want to switch to a bank that does -- consider a service such as Mint.com that aggregates all your bank account data.

"These services are a backdoor mobile capability that allows you to go mobile even if your bank isn't there yet," Bissell says. The service allows a user to access his or her bank records via cellphone. However, bill payments and money transfers are restricted. While services such as Mint.com don't get customers all the way to mobile banking, Bissell says it can be a good makeshift solution until the customer's bank does offer it.