Alongside his continued voice acting on The Simpsons, Azaria became more widely known through his live-action supporting appearances in films such as Quiz Show (1994), Heat, The Birdcage (1996) (for which he won a Screen Actors Guild Award) and Godzilla (1998). He has also appeared in numerous films including Mystery Men (1999), America's Sweethearts (2001), Shattered Glass (2003), Along Came Polly (2004), Run Fatboy Run (2007), Night at the Museum: Battle of the Smithsonian (2009) and The Smurfs (2011) and The Smurfs 2 (2013). Further voice roles include Anastasia (1997), for which he won an Annie Award.
His live-action television work includes recurring roles on the sitcoms Mad About You and Friends, as well as dramatic roles in the TV films Tuesdays With Morrie (1999) as writer Mitch Albom and Uprising (2001) as Jewish resistance leader Mordechai Anielewicz. For the former, Azaria received the Primetime Emmy Award for Outstanding Supporting Actor in a Limited Series or Movie. He starred in the title roles in the Showtime drama series Huff (2004β2006) and the IFC sitcom Brockmire (2017β2020). His recurring role on the drama Ray Donovan earned him a sixth Primetime Emmy Award in 2016.
Azaria made his Broadway debut as Lancelot in Spamalot, for which he was nominated for the Tony Award for Best Actor in a Musical. He returned to Broadway in 2007, playing David Sarnoff in The Farnsworth Invention.