I don't think banks really help me manage my money. They might store it securely, give me interest, enable transactions, and offer statements, but that's a short list of services - it's not the whole picture.
For example: what about allowing tagging and categorizing of each statement entry, so I can see how much I spend in the supermarkets or on the gas bill each month?
What about helping me with my tax? Or offering reporting and trending? Or providing financial planning tools? Or customized email / SMS alerts (or even customized financial transfers) when I reach various thresholds?
Drill-down and comparisonI've got online accounts with various different utilities and retailors, but I've forgotten many passwords and don't get around to visiting them very often.
So, imagine if I could click an entry in my statement, and be taken to the relevant website - e.g. click on an entry from the water company, to see my online account there. It just requires my bank to know the URL for common providers (or even store my usernames and passwords).
That way, my bank is truly helping me organize my finances and track my expenditure. It's moving from offering basic banking services to helping me manage my bills.
I could even pick a utility or shop, and view a timeline with all the money I'd spent there. It could link to a shopping comparison site, to help me understand the competition.