ICICI Bank is providing a mobile app iMobile for its customers. The App is available as java app for all symbian mobiles, and there is also an iPhone version of the same. (Check here whether your device is supported). ICICI Bank is the first bank in India to provide such a useful iPhone app.
Update: ICICI iMobile Android app is now available. More details.
In order to use iMobile, you should first have registered for mobile banking. Then, for activating iMobile, send an SMS from the registered number saying imobile to 5676766. You will get an activation code, which is need to activate the iMobile app.
Even though you should have registered for Mobile banking, the app need not be installed in the registered phone. You can install in any iPhone / iPod touch.