Rain Man won the Academy Award for Best Picture for the 1988 film year. The award was presented at the 61st Academy Awards ceremony on March 29, 1989, but the eligible film year was 1988. That distinction explains why some references mention 1989 while the correct answer to this question is 1988.
Directed by Barry Levinson, Rain Man stars Dustin Hoffman as Raymond Babbitt and Tom Cruise as his younger brother, Charlie. The drama follows the brothers as they travel together and gradually develop a relationship after Charlie discovers Raymond’s existence and extraordinary mathematical abilities.
Rain Man received eight nominations and won four Oscars: Best Picture, Best Director for Levinson, Best Actor for Hoffman, and Best Original Screenplay. It was also a major commercial success, becoming the highest-grossing film released in the United States in 1988.
The common mix-up is between the film year and ceremony year. The 61st Oscars took place in 1989, but the Academy honored movies released during 1988, so “1988” is the canonical answer.