Recently my local bank (Kiwibank in NZ) launched a free online financial management service that I've been very impressed with. It automatically categories all my expenses and makes it easy to see where my money is going and set a budget. It also has an intuitive interface which is rare for a bank.

This page gives an overview of its features: http://www.heaps.co.nz

Aside from that banks should be aiming to make as many of their services as possible available online. Little things like setting up a new account should not require me go in to the bank just to fill out a form when the same process could be done online in only a few simple steps.