Charlie Babbitt (Tom Cruise), a Los Angeles car dealer in his mid-twenties, is in the middle of importing four grey market Lamborghinis. The deal is being threatened by the EPA, and if Charlie cannot meet its requirements he will lose a significant amount of money. After some quick subterfuge with an employee, Charlie leaves for a weekend trip to Palm Springs with his girlfriend, Susanna (Valeria Golino).
Charlie's trip is cancelled by news that his estranged father, Sanford Babbitt, has died. Charlie travels to Cincinnati, Ohio, to settle the estate, where he learns an undisclosed trustee is inheriting $3 million on behalf of an unnamed beneficiary, while all he is to receive is a classic Buick Roadmaster convertible and several prize rose bushes. Eventually he learns the money is being directed to a mental institution, which is the home of his brother with autism, Raymond (Dustin Hoffman), of whose existence Charlie was previously unaware. This leads Charlie to ask the question that permeates the movie: "Why didn't somebody tell me I had a brother?"
Although Raymond has autism, he also has superb recall, albeit usually with little understanding of the subject matter, and extreme skill in mathematics. He is said to be a savant by some doctors. He is frightened by change and adheres to strict routines (for example, his continual repetition of the "Who's on First?" sketch). Except when he is in distress, he shows little emotional expression and avoids eye contact. Numbed by learning that he has a brother and determined to get what he believes is his fair share of the Babbitt estate, Charlie takes Raymond on what becomes a cross-country car trip (due to Raymond's fear of flying) back to Los Angeles to meet with his attorneys. Charlie intends to start a custody battle in order to get Raymond's doctor, Dr. Gerald R. Bruner (Jerry Molen), to settle out of court for half of Sanford Babbitt's estate so that the mental institution can maintain custody of Raymond. Susanna, disgusted by Charlie's self-centeredness and his attempts at using his brother as a pawn to gain the money, leaves Charlie in Cincinnati and disappears.
During the course of the journey, Charlie learns about Raymond's autism, which he initially believes is curable — resulting in his frequent frustration with his brother's antics. He also learns about how his brother came to be separated from his family, as a result of an accident when he was left alone with Charlie when Charlie was a baby. Raymond also sings "I Saw Her Standing There" by The Beatles like he did when Charlie was young, prompting Charlie to realize that Raymond is the protective figure from his childhood, whom he falsely remembered as an imaginary friend named "Rain Man." Charlie proves to be sometimes shallow and exploitative, as when he learns that Raymond has an excellent memory and takes him to Las Vegas to win money at blackjack by counting cards. However, towards the end of their trip Charlie finds himself becoming protective of Raymond, and grows to truly love him.
Charlie finally meets with his attorney to try to get his share of his inheritance, but then decides that he no longer cares about the money and really just wants to have custody of his brother. However, at a meeting with a court-appointed psychiatrist and Dr. Bruner, Raymond is unable to decide exactly what he wants. Eventually, the psychiatrist presses Raymond to make the decision, upsetting him and leading Charlie to request that the doctor back off. Raymond is allowed to go back home to Cincinnati. Charlie, who has gained a new brother and mellowed considerably, promises Raymond as he boards an Amtrak train that he will visit in two weeks.