People on the left like Paul Krugman sometimes suggest that 1934-80 was a sort of golden age of stable banking---after the New Deal regulatory reforms and before the deregulation of the 1980s. I'm not convinced that regulation has much to do with this period of stability, for two reasons:
1. Banking was already getting unstable towards the end of this period, as the cost of small deposits rose above the interest rates that banks and S&Ls earned on their 30-year mortgages.
2. Unexpected price level increases during 1933-80 helped borrowers and reduced debt defaults.
The US devalued the dollar from $20.67/oz to $35 an ounce between 1933 and 1934. This led to a large one-time increase in the price level, which was spread out over many years. In addition, changes in the monetary system reduced the demand for gold, which further increased prices. (For instance, it became illegal for Americans to hoard gold.) The net effect was a large, one-time increase in the price level between 1933 and 1968.
After 1968 the price of gold started rising in global markets, which meant that we were essentially on a pure fiat money regime. Inflation rose even higher during the 1968-81 period than during the previous 35 years. Much of this inflation was unexpected. Borrowers often had long-term loans that did not reflect the ex post rate of change in prices, and hence borrowers did very well. Mortgage loan defaults were not very common.
After 1980-81, both inflation and NGDP growth slowed sharply and unexpectedly. Now borrowers were hurt, as the interest rates they agreed to in the late 1970s and early 1980s were far higher than the rate of inflation after 1982.
[Note that the mild deflation of 1949 didn't do much harm because back in those days deflation was expected after the end of major wars.]
Even though borrowers did well during the post war decades, banks were under increasing stress in the 1970s. In the 1950s and 1960s they had lent money long-term at fairly low rates, and then when inflation rose in the 1970s they had to pay much higher rates to attract short-term deposits. I've seen estimates that much of the banking system was technically bankrupt around 1980, if all the assets were marked to market. Policymakers saw this problem, and decided to deregulate to so that banks and S&Ls could have a more diversified balance sheet. This may have backfired as "zombie thrifts" that were protected by FDIC and FSLIC engaged in a sort of "double or nothing" strategy. Since they were already in dire straits, why not gamble with taxpayer funds? They had little to lose and a lot to gain. (And yes, FDIC funds most definitely are taxpayers' money, even if these organizations are not formally bailed out. Their resources come from a tax on banks. And FSLIC was bailed out.)
The tight money policy adopted in 1981 led to much lower inflation and interest rates over time, which fixed the maturity mismatch problem. But it also led to many more loan defaults. If the Fed had adopted a tight money policy in the 1970s, it is very likely that we would have had a severe banking crisis then, even though "deregulation" had not yet occurred. Most of the bad behavior that got banks into trouble (subprime loans, mortgage-backed debt, etc.) has always been legal. That's not to say that regulatory changes after 1980 did no harm, for instance many of the changes actually encouraged sub-prime lending. But banking crises can occur in even highly regulated banking systems, as long as inflation and NGDP growth falls sharply and unexpectedly.