"George Carlin was a hugely influential force in stand-up comedy," Stiller, 42, said in a statement. "He had an amazing mind, and his humor was brave, and always challenging us to look at ourselves and question our belief systems, while being incredibly entertaining. He was one of the greats and he will be missed."
Carlin, 71, died Sunday of heart failure.
Staff members of Saturday Night Live and David Letterman's Late Show are said to devastated by the loss, a former associate of both programs tells PEOPLE.
Comic actor-writer Marshall Efron – a friend who recalled Carlin as "a nice guy" – tells PEOPLE that he once "received a check out of the blue from George, simply because he'd used [in his act] a funny line he'd heard me say."
"If there was ever a comedian who was a voice of their generation it was George Carlin," said Leno, who frequently had Carlin on the Tonight Show (a venue on which Carlin started appearing in the 1960s).
"Before George, comedians aspired to put on nice suits and perform in Las Vegas. George rebelled against that life. His comedy took on privilege and elitism, even railing against the game of golf."
Despite the passage of years, said Leno, 58, "He never lost that fire. May he continue to inspire young people never to accept the status quo."
"Nobody was funnier than George Carlin," Knocked Up and The 40-Year-Old Virgin director Judd Apatow, 40, told the Associated Press. "I spent half my childhood in my room listening to his records experiencing pure joy. And he was as kind as he was funny."
Carlin's Loving DaughterThe comic's own daughter, Kelly Carlin, 45, said, "Most people know George Carlin as an icon of comedy and an advocate of free speech. I just know him as Dad ... and what a dad he was."
The New York-born funnyman "taught me the value of speaking the truth in a world that doesn't always want to hear it and gave me the gift of laughter," she said. "He was loved and revered by so many and will be missed beyond words – but never forgotten."
Besides Kelly, George Carlin is survived by his wife, Sally Wade; son-in-law, Bob McCall, brother, Patrick Carlin and sister-in-law, Marlene Carlin. (His first wife, Brenda Hosbrook, died 11 years ago.)
Added Kelly Carlin: "Our family wishes to thank everyone who has sent love and support our way. Your kind words and thoughts are bringing much comfort to us during such a difficult time."