The nation's banks had their worst year since the Great Depression in 1984, and regulators faced their greatest tests since the Federal Deposit Insurance Corp. was founded in 1933 to restore investor confidence in the banking system.

If the economic recovery continues to chug along in 1985, the banking system should recuperate from the aftereffects of the back-to-back recessions of the early 1980s. The decline in interest rates has helped boost bank profits -- banks usually lower their lending rates more slowly than their cost of funds declines -- and should also make it easier for some of their troubled borrowers to make their payments.

But had 1984 run true to historical form, the banking industry should have been well on the road to recovery long ago.

Instead, there were 79 bank failures, more than in any year since the FDIC was founded, and scores of banks were added to the regulators' list of banking institutions with inordinate problems. About 820 banks are now on the FDIC's list, about twice as many as were there during the worst days following the 1974-75 recession.

William M. Isaac, chairman of the Federal Deposit Insurance Corp., said that many banks are coming off the list thanks to the continuing economic recovery, which enables many problem borrowers to resume making loan payments on schedule.

But the growing problems in agriculture are forcing regulators to put farm banks on the problem lists at a faster clip than non-farm banks are coming off. Another steep decline in oil prices could revive a crisis among banks that specialize in energy lending.

The most vulnerable areas in banking today are energy and agriculture: energy-related loans are still weakening the overall quality of loan portfolios at many banks that are not energy lending specialists. The huge loans the nation's bigger banks have made to economically strapped developing countries exacerbate the worries the regulators, as well as the general public, have about the quality of bank loan portfolios.

Bank examiners recently have been far tougher than in recent memory: both in assessing the quality of loans and in requiring many banks to divert a large portion of their income stream to loan loss reserves. The loan reserves and capital are the final bulwark to absorb loan losses.

The regulators -- the FDIC, the Comptroller of the Currency and the Federal Reserve Board -- have become far more concerned with increasing bank capital than they have been in years. Many banks, including the giant money center banks of New York, Chicago and California, are becoming more conservative, even without the prodding of the regulators.

Undoubtedly, the biggest shock to regulators and bankers alike was the 80th 1984 bank failure -- the one that did not appear on the formal list of failures. Continental Illinois National Bank, based in Chicago, was the nation's eighth-largest when a massive run on its worldwide deposits threatened to sink it. Had not the Federal Reserve stepped in with the biggest business rescue package in history -- about $4.5 billion -- Continental's de facto failure would have been real.

The threat of a global financial panic induced not only regulators but 28 of Continental's biggest bank competitors to pump in funds to replace lost deposits and absorb the huge losses in the bank's loan portfolio.

It was the biggest challenge the FDIC, and its $17 billion insurance fund, had ever faced. The ultimate cost to the government of the Continental rescue cannot yet be calculated. But the $41 billion in assets possessed by Continental exceeded by more than two times all of the assets of all of the banks that have failed in the 50-year history of the agency.

Since the Continental crisis last summer, bank after bank has taken special charge-offs to cover previously unpublicized loan problems and agreed to boost capital or improve management.

The problems of the nation's money center banks -- with their global reach and global troubles -- undoubtedly will garner the bulk of public and regulatory attention in 1985. The crisis in Latin America has been muted -- but the economic and social problems of the region have not evaporated.

These giant banks are far more vulnerable to the kinds of rumors that spawned the massive run on Continental Illinois, and the potential systemwide tragedies from a demise of a money center bank dwarf the damage that could be done by the failure of several hundred smaller institutions.

A further, especially sudden, decline in oil prices would hurt money center banks (energy loans were the source of Continental's major loan problems) but would strike more deeply at the regional banks that specialize in lending to oil drillers, oil producers and the companies that service energy exploration and development.

New problems in the energy sector, however, are only potential problems. The crisis among agricultural banks, mainly smaller and rural, is here.

The depression in American agriculture shows no signs of abating. Farm borrowers are defaulting in increasing numbers. For many farmers who have hung on in the last four years, last year may have been their last. For a number more, 1985 undoubtedly will be unless farm fortunes change.

Farm banks traditionally have been far more capitalized than their big city cousins. But even these banks -- many of which have 75 to 80 percent of their loans in agriculture or to industries and individuals dependent upon the health of the farm sector -- are seeing their once-sturdy capital cushion eaten up.

But most banks and bank borrowers will benefit by the recent decline in interest rates. Money center banks, which "buy" most of their deposits in the open market, have already seen their margins widen. Banks can lower their prime rates more slowly than the deposit costs fall.

Each decline in the prime rate -- it has fallen 2 1/4 percentage points in the last few months -- reduces the debt cost to businesses. In most cases, the lower rates mean less strain. But in a number of cases, among borrowers banks worry most about, the lower borrowing costs may mean survival.