Goldman Sachs Group Inc.—one of the few Wall Street titans to thrive during the financial crisis—was charged with deceiving clients by selling them mortgage securities secretly designed by a hedge-fund firm run by John Paulson, who made a killing betting on the housing market’s collapse.

Goldman vigorously denied the Securities and Exchange Commission’s civil charges, setting up the biggest clash between Wall Street and regulators since junk-bond king Drexel Burnham Lambert succumbed to a criminal insider-trading investigation in the 1980s, helping to define the era. “The SEC’s charges are completely unfounded in law and fact,” Goldman said in a statement, promising to “contest them and defend the firm and its reputation.”