First Broadway, Next the World
Mike Nichols (born Mikhail Igor Peschkowsky, but who's keeping track?) was a successful comedian, actor, and Broadway director before he morphed into a Hollywood force. He'd directed a bunch of Neil Simon plays, and had performed as a wildly successful satirical comedy duo with Elaine May.
By the time he was tapped to direct The Graduate, he'd already brought his theatrical sensibility to the big screen with the movie version of Edward Albee's hit play, Who's Afraid of Virginia Woolf? That was in 1966, the year before The Graduate came out.
In crafting the film, Nichols said he was inspired by the character John Marcher in Henry James' famous short story, The Beast in the Jungle. Marcher is kind of like Benjamin Braddock in that neither know what they want to do with their futures, but they know that they want them to be "different." Yet whereas—spoiler alert—Marcher lives his whole life without anything really happening to him, failing to seize love when the moment presents itself, Braddock does (eventually) seize the day, pursuing Elaine Robinson despite various impossible obstacles. Nichols also decided to have Mrs. Robinson wear jungle-cat print clothing to make her look like a predator playfully stalking her prey (Benjamin), or like the metaphorical "Beast" of James' story.
Nichols also made important casting choices: he thought about giving Benjamin's part to Robert Redford, but decided Redford couldn't play an underdog, since he'd apparently never "struck out" with a girl. Choosing an actor like Hoffman was a risk; he wasn't someone with leading-man looks or demeanor. He and Turman cycled through and dispensed with many actresses for the role of Mrs. Robinson before finally settling on Anne Bancroft. By unanimous opinion, they made the right choices. (Source)
Eats Spam and Jam and Ham a Lot
The Graduate defines everything people came to expect from Mike Nichols' directorial style: great acting, laughs, and a subversive edge. Later Nichols' movies with those same qualities included Catch-22 (also with Buck Henry as a screenwriter) and Carnal Knowledge, with Jack Nicholson and Art Garfunkel (who, as half of Simon and Garfunkel, performed on The Graduate's famous soundtrack). He also continued his conquest of Broadway, racking up Tony Awards, and directing smash-hits like the 2005 Monty Python musical Spamalot.
Nichols was still going strong when he died in 2014. After his death, people who weren't all that familiar with his work read the obit and asked "Is there anything he didn't write or direct?" Nichols eventually won 4 Emmy awards and 8 Tonys and was one of only a dozen "EGOT" artists who won the award world's Grand Slam—an Emmy ("Wit"), Grammy ("An Evening with Mike Nichols and Elaine May"), Oscar (The Graduate), and Tony (Barefoot in the Park). (Source) Add to that a Kennedy Center Honor and the American Film Institute's Life Achievement award, and you're looking at show-biz history. Yowza.
(Bonus fact: Mel Brooks, the real-life husband of Mrs. Robinson (Anne Bancroft) was another EGOT-ist.)