He died in hospital in Danbury, Connecticut, near where he lived.
Sendak, who was born in New York, wrote some 17 books and illustrated dozens more.
In addition to Where the Wild Things Are (first published in 1963), some of his best-loved stories included Chicken Soup with Rice (1962), Higglety Pigglety Pop!, Or: There Must Be More to Life (1967) and In the Night Kitchen (1970).
As well as multiple children's prizes, Sendak was awarded a National Medal of Arts in 1996 for his contribution to American literature.
"I don't write for children," he told Stephen Colbert in one of his final interviews, in January (video below). "I write. And somebody says, 'That's for children.' I don't set out to make children happy, or make life better for them, or easier for them. [...]
"I like them as few and as far between as I like adults – maybe a bit more, because I really don't like adults, at all."
Sendak's final work, titled My Brother's Book, will be published posthumously in February 2013, according to the Times. It is described as a poem inspired by his late brother.