Norton has been acting for over forty years in theatre, television, and movies, and frequently plays clergymen, most notably Bishop Brennan in the sitcom Father Ted, as well as roles in The Sweeney (1975), Peak Practice (1993), Sunset Heights (1997), A Love Divided (1999), Rebus: Black and Blue (2000), Mad About Mambo (2000), Boxed (2003) and Jimmy's Hall (2014).
He starred as Finian McLonergan in the critically acclaimed New York City Center's 2009 production of Finian's Rainbow, and in October 2009 reprised the role in the Broadway revival at the St. James Theatre. His co-stars were Cheyenne Jackson (Woody) and Kate Baldwin (Sharon).
One of Norton's earlier UK television roles was as the timid Gardener in the first series of the long-running CITV children's series T-Bag, ('Wonders in Letterland').
As well as Bishop Brennan in Father Ted, Norton also played Albert Einstein in two episodes of Star Trek: The Next Generation; as the librarian Lieutenant James Porteous in an edition of the highly acclaimed 1970s British television drama series Colditz; Harrister, a criminal involved in an intricate bank robbery in The Sweeney episode; Contact Breaker, as O'Brady in Minder, episode; National Pelmet and Rory, a roguish but genteel Irishman, who is diagnosed with cirrhosis of the liver in The Royal episode; Beggars and Choosers.
Norton has appeared in two episodes of Van der Valk. On Babylon 5 he appeared in a number of roles including "Ombuds Wellington" in 1994 episodes "Grail" and "The Quality of Mercy"; a Narn ("Dust to Dust", 1996); and Dr. Lazarenn, a Markab doctor in "Confessions and Lamentations" (1995). In Fall of Eagles he played Alexander Kerensky.
Other television work includes; Agatha Christie's Poirot, Waking the Dead, Cheers, Frasier, Midsomer Murders, Maigret and Rumpole of the Bailey as "Fig Newton", Stan Laurel in the BBC drama Stan and Larry Joyce in the 2013 television drama Deception
He appeared in the 1969 epic film Alfred the Great as Thanet.
Norton played the part of "Pongo" in the screen version of Spike Milligan's war-time memoir 'Adolf Hitler. My Part in his Downfall.' In 1971 he played "Chris Cawsey" (aka "The Rat Man"), one of several villains in the controversial Sam Peckinpah movie Straw Dogs starring Dustin Hoffman. His character had a deviously infectious, deliberately irritating laugh that helped build tension throughout the film.(see external links)
He appeared in the movie Memoirs of an Invisible Man alongside Chevy Chase in 1992.
He appeared in the 1992 Irish-made film Into the West.
He appeared in the comedy On the Nose as Patrick Cassidy, along with Dan Aykroyd and Robbie Coltrane, in 2001.
He appeared in a brief cameo in Harry Potter and the Chamber of Secrets in 2002 as Mr. Mason.
He played an Irish immigrant in the 2005 Australian/UK co-production, The Oyster Farmer.
He played title role of Stan Laurel in the 2006 TV movie Stan, based on Neil Brand's radio play of the same name.
He played Herr Lizst in the 2008 holocaust film The Boy in the Striped Pyjamas.
In 2011 he appeared as the character Old Mr Black in the film Extremely Loud and Incredibly Close directed by Stephen Daldry.
Norton appeared in the 2011 film Water for Elephants, in which he portrays a circus worker called "Camel" who befriends a character played by Robert Pattinson.
In 2012 he appeared as the character Tommy in the short film Homemade written by Matthew Roche and directed by Luke McManus.
Norton's most recent film credit is in the Ken Loach film Jimmy's Hall which was released in 2014.
He plays the role of Mr. Heelshire in 2016 film The Boy.
Norton has a longtime partnership with playwright Conor McPherson, having originated roles in six of his plays in Dublin, London and New York, and for which he has won both the Tony and Olivier Award. Norton played Jack in The Weir (1997), Joe in Port Authority (2001), Matthew in Come on Over (2001), Richard in The Seafarer (2006–7), Reverend Berkeley in The Veil (2011), and Maurice in The Night Alive (2013).
In 2004 he took part in the touring production of Martin McDonagh's The Pillowman.
In 2006/7 he appeared in Conor McPherson's The Seafarer at The National Theatre, and reprised the same role in the 2008 Broadway theatre production of the play.
In 2012, he performed as The Chairman in a Broadway adaptation of The Mystery of Edwin Drood.
In 2013/2014 he played Maurice in Conor McPherson's The Night Alive, a Donmar Warehouse production, transferred to the Atlantic Theatre Company in New York.
Norton starred as Candy in the 2014 Broadway revival of John Steinbeck's Of Mice and Men (alongside James Franco and fellow Irishman Chris O'Dowd) at the Longacre Theatre. In 2016, he played Giles Corey in Ivo van Hove's production of Arthur Miller's The Crucible at the Walter Kerr Theatre.
Norton provided the voice for Major Kennet for the 2003 Doctor Who animated serial, Scream of the Shalka.
He has recorded the whole of James Joyce's Ulysses (with Marcella Riordan), Dubliners, Finnegans Wake (abridged with Marcella Riordan) and A Portrait of the Artist as a Young Man for Naxos Records.
The Third Policeman by Flan O'Brien 2009.
Thorndyke: Forensic Investigator: for BBC Radio 4 Extra 2011.
BBC Radio production of 'The Mustard Seed' by Nick Warburton
The House on the Borderland by William Hope Hodgson: BBC Radio 4 Extra, May 2012
Mr Deasy in Ulysses: BBC Radio 4 production for Bloomsday 16 June 2012
Narrator: The Stack, short story by Rose Tremain, broadcast on BBC Radio 4 Extra, 24 September 2012.
Death in BBC Radio 4 production of Good Omens by Terry Pratchett and Neil Gaiman, December 2014.Jacob's Awards – Solo, for Telefís Éireann in 1964 in which he played a gay man.
Legend Award – as the older Stan Laurel in a television docudrama about Laurel and Hardy. (Elk Acting Festival, Dundonald, Belfast). Norton did not appear as he did not expect to win the award.
Olivier Award – Best Actor in a Supporting Role for The Seafarer
Tony Award – Best Featured Actor in a Play for The Seafarer