Lumet's death was confirmed by relatives and friends, who said he died yesterday morning at his Manhattan home. He had suffered from lymphoma.
A Philadelphia native, Lumet moved to New York City as a child and it became the location of choice for more than 30 of his films. Although he freely admitted to a lifelong love affair with the city, he often showed its grittier side.
"Dog Day Afternoon" told the true-life story of two social misfits who set in motion a chain of disastrous events when they tried to rob a New York City bank on an oppressively hot summer afternoon.
"It's not an anti-L.A. thing," Lumet said of his New York favoritism in a 1997 interview. "I just don't like to live in a company town."
He did receive an honorary Oscar in 2005 for lifetime achievement. He also received the Directors Guild of America's prestigious D.W. Griffith Award for lifetime achievement in 1993.
"If you prayed to inhabit a character, Sidney was the priest who listened to your prayers, helped make them come true," the actor said.
The composer Quincy Jones, who scored music for five of Lumet's films, said, "Sidney was a visionary filmmaker whose movies made an indelible mark on our popular culture with their stirring commentary on our society."
Lumet immediately established himself as an A-list director with his first theatrical film, 1957's "12 Angry Men," which took an early and powerful look at racial prejudice as it depicted 12 jurors trying to reach a verdict in a trial involving a young Hispanic man wrongly accused of murder. It garnered him his first Academy Award nomination.
Other Oscar nominations were for "Dog Day Afternoon" (1975), "Network" (1976) and "The Verdict" (1982).
"Network," a scathing view of the television business, proved to be Lumet's most memorable film and created an enduring catch phrase when crazed newscaster Howard Beale exhorted his audience to raise their windows and shout, "I'm mad as hell, and I'm not going to take it anymore!"
Lumet's resume also included films based on noted plays including Tennessee Williams' "Orpheus Descending," which was made into "The Fugitive Kind."
He is survived by his wife, journalist Mary Gimbel, daughters Amy and Jenny Lumet, nine grandchildren and a great-granddaughter.