While most poor and middle class people were heavily affected either directly or indirectly due to layoffs, lack of job opportunities, bank failures, and foreclosures, for the wealthy, it largely depended on how you had your money invested.
One notable example is the case of Groucho Marx. Both he and his brother Harpo had invested their money almost entirely in the stock market in the late 1920s because the market was booming. In May 1929, five months before the crash, Groucho even wrote an essay for the New Yorker about his investments entitled "Buy It, Put It Away, and Forget About It".
When the stock market crashed, he lost everything. All $240,000 of it. (That's about $3.3 million in 2017 dollars.) That was an enormous fortune for somebody who, up until that point, had only ever been a stage actor. He would claim later that this event brought on insomnia that he battled the rest of his life.
Joseph Kennedy, father of John F. Kennedy and Robert Kennedy, on the other hand, made out like a bandit. In the mid-1920s, he had heavily invested in a movie studio called Film Booking Office of America. In 1928, he helped arrange a merger between FBO, the Keith-Albee-Orpheum chain of vaudeville theaters, and RCA (Radio Corporation of America) who had developed a sound film technology but had no movie studio nor theater chain with which to use it. In the process of arranging this merger, Kennedy sold off his shares of stock in FBO to this newly-formed company called RKO (who would go on to be one of the major Hollywood studios from 1930 to 1955), and divested himself of much of his other stock as well. The merger was completed by mid-1929, just before the stock market crashed.
In David Nasaw's book about the Joseph Kennedy, The Patriarch, he wrote:
"He had entered the [film] industry a rich man but departed a multimillionaire...On November 30, 1926, after ten months in the film business, his 'capital account' held $373,394 and his real estate holdings were limited to his modest house in Brookline. Less than three years later, on October 31, 1929, after the stock market crash, his capital account held $1,740,494 (more than $22 million today) and he had bought two new houses for the family. His net worth was five times what it had been three years earlier. And that doesn't take into account his real estate holdings."
So while many of Kennedy's business associates were losing money hand over fist, still being heavily invested in the market, he retained most of his fortune. He was thus able to buy real estate and other investments cheaply from others who were selling it off in order to stave off their stock market losses.
Joseph Kennedy did so well that John F. Kennedy, who was twelve years old at the time of the crash in October 1929, later claimed he didn't learn about the Great Depression until he read about it in books when he went off to Harvard in the fall of 1936.
Others with insider information also came out of it relatively unscathed. Albert Wiggin, president of Chase Bank, began selling off his stock in the bank he ran in September 1929 and made $4 million before the crash hit, while publicly committing his bank to investment in the market. Others, like oil magnate J. Paul Getty, were able to buy commodities on the cheap after the crash and build a fortune as the market eventually returned to their Roaring Twenties heights over the next couple decades.
Contrast that to wealthy economist Irving Fisher, or to General Motors co-founder William C. Durant who went from multimillionaire status before the crash to flat broke by 1936. Even worse was the case of the Studebaker car company's president Albert Erskine. His company lost it all in the early years of the crash, in which he was heavily invested, and he committed suicide in 1933.