Forbes has a fascinating article by Laurence J. Kotlikoff and Edward Leamer, with fundamental thinking about banks.
They trace the problems of banks to the fundamental contradictions of having a highly leveraged financial firm, with assured returns and full liquidity for depositors, and opaque + illiquid assets. I agree with this gloomy prognosis. A more fleshed out argument is in this pair of articles -- link and link -- which were opinion pieces in 1999.
I stopped chasing those lines of thought because it seemed dishearteningly hard, trying to sell a world without banks as we know 'em. But if you are persuaded by these arguments, then you will like a world where we do more finance through securities markets, through `defined contribution and NAV-based' financial firms (i.e. direct household participation in financial markets, mutual funds and DC pensions), and less through `assured returns' financial firms such as banks, DB pensions and insurance companies.
In a perverse way, India's prodigous mistakes of policy on banking have helped steer the country into a more market-dominated financial system, which has helped build a better financial system.
Since we're unlikely to reconstruct the economy in radical ways, we have to confront the problems of banks. I feel the most important element of safe and sound banking is: a proper deposit insurance mechanism. Chapter 6 of Raghuram Rajan's report is the best blueprint out there about setting up a deposit insurance corporation, and other dimensions of improving systemic risk (see `V. Preventing Crisis and Dealing with Failure').
You might like to also see this picture on banking reforms.