While there aren't as many examples of malware out in the mobile device market as there are on traditional PCs, the fact remains that mobile devices are just specialized computers. That means it's possible for someone to design an app that could try to access your information. One way this could happen is if the app hides a keylogger.
A keylogger is a program that records -- or logs -- keystrokes. Every letter or number you enter into your phone could be recorded. If a hacker pairs a keylogger with some code that either sends off an e-mail or text message at certain times of the day, you might be sending all your keystrokes to someone anywhere on the globe.
For the moment, mobile devices are less prone to malware attacks than computers. But you should still be careful when downloading apps -- not just your banking app, but all apps. Do a little research before you download that next widget or game to make sure the app developer has a good reputation. And if you've jailbroken an iPhone or you've sideloaded unapproved apps, be aware that your data could be vulnerable.