Norton has been nominated for four Academy Awards for his performances as a murder suspect in Primal Fear (1996), a neo-Nazi leader in American History X (1998), an egotistical actor in Birdman (2014), and singer-songwriter Pete Seeger in A Complete Unknown (2024).

He won the Golden Globe Award for Best Supporting Actor – Motion Picture for his role in Primal Fear (1996) and was Globe-nominated for Birdman (2014) and A Complete Unknown (2024).

He won the Screen Actors Guild Award for Outstanding Cast in a Motion Picture with the ensemble of the Wes Anderson comedy The Grand Budapest Hotel (2014).

For his work on television, he received a Primetime Emmy Award for Outstanding Documentary or Nonfiction Special nomination for the HBO documentary By the People: The Election of Barack Obama (2009).

He was also nominated for the Daytime Emmy Award for Outstanding Performer in Children's Programming for the Netflix animated children's program Ask the StoryBots (2019).