What steps has today's banking industry taken to prevent another Great Depression?
I believe there is an implicit assumption in your question that presumes the banking industry was somehow to blame for the Great Depression in the first place. Please see the "Ask the Economist" archives question on the gold standard and the Great Depression for a more in-depth explanation of the real causes of the Depression.
For the purposes of answering this question, suffice it to say that the fault lies in a source other than the private (though heavily regulated) banking system. The nation's central bank, the Federal Reserve System, grossly mismanaged the money supply, first expanding it excessively and producing an unsustainable boom in the 1920s, then presiding over a radical contraction of the money supply from 1929-1933. For a very detailed analysis of that disastrous policy, I recommend Murray Rothbard's classic book, America's Great Depression.
Then in 1930, Congress and the White House radically raised tariffs, precipitating a world trade war and a serious collapse in U. S. export industries, especially agriculture. In 1932, Congress and the White House doubled the income tax. Then Franklin Roosevelt's "New Deal" prevented recovery for eight years through its costly and counterproductive policies.
The underlying cause of the business cycle is money and credit expansion that is artificial, that is, prompted by political manipulation of interest rates and bank reserve requirements. Banks today have only marginal control over such things and for the most part, must be responsive to genuine market conditions. A general, economy-wide excessive expansion of credit and currency is the result of a centrally orchestrated policy of the Federal Reserve, not of individual banks.
Perhaps a more detailed explanation of the Great Depression and all of the regulatory manifestations that created and prolonged it would be of interest to you and would further answer your question. We have produced an essay here at the Mackinac Center that provides just that, in more detail than what appears on our Web page. Just call 1-800-22-IDEAS and ask for a copy of "Great Myths of the Great Depression."