Some of the clearest analyses of banking principles come from the 19th century, when a general awareness of various banking options still existed. Today, with the nationalization of note issues and the ubiquity of fiat currencies and central banking, few remember the alternatives or understand the implications of our current system. A French economist, Charles Coquelin, wrote a number of lucid works, including a comprehensive analysis of credit and banks (in French).
In a shorter article by the same author explaining the role of credit in economic crises, Coquelin explains that only economies that use credit experience periodic crises, and that such crises are acerbated considerably in economies with central banks. While in 1864, the possibility of fiat currency didn't cross his mind, he could still see that the central banks of his day (e.g., Bank of England & Banque de France) distorted credit markets by their privileged status. With specific privileges beyond all other banks, central banks were considered more secure than private banks, and could both borrow and lend at lower rates of interest than their private counterparts as a result. This left largely riskier borrowers for the private banks and led inexorably to de facto national currencies which linked problems with one bank to those of others.
While there will (and should) always be periodic bank failures, as in any other industry, it is important that the full risks and losses of such failures be left with the investors and depositors of such banks so as to avoid taxing healthier banks to support their less healthy neighbours. In a free market, marginal institutions fall first and as their assets liquidated, healthier banks can buy them at discounted prices and shore up their own portfolios. This leaves the healthiest institutions standing at the end of the crises.
Alas, we have adopted the exact opposite policy in the current crisis. The weakest banks that fall first are bailed out by governments, along with every subsequent bank until the government can no longer issue more promises against future tax revenue. At that point, all of the "salvaged" banks fall at once when the government defaults on their debt obligations. Perhaps Coquelin was right in suggesting that the whole process is less painful if left to the free market.