Some films I don't think one could/should ever do a remake of …. and the roles I can't imagine being played by anyone else. There are undoubtedly lots more in both categories.

Matt Damon Jason Bourne the Jason Bourne series
2002
Viggo Mortensen Aragorn "Lord of the Rings"
2001
Russell Crowe Maximus "Gladiator"
2000
Julia Roberts Anna Scott "Notting Hill"
1999
Hugh Grant William Thacker "Notting Hill"
1999
Emma Chambers Honey "Notting Hill"
1999
Anthony Hopkins Dr. Hannibal Lector "The Silence of the Lambs"
1991
Julia Roberts Vivian "Pretty Woman"
1990
Robin Williams John Keating "Dead Poets' Society"
1989
Alan Rickman Hans Gruber "Die Hard"
1988
Bruce Willis John McClane "Die Hard"
1988
Patrick Swayze Johnny Castle "Dirty Dancing"
1987
Meryl Streep Karen Blixen "Out of Africa
1985
Geoff Bridges Starman "Starman"
1984
Rutger Hauer Roy Batty "Bladerunner"
1982
Harrison Ford Indiana Jones "Raiders of the Lost Ark"
1981
Karen Allen Marian Ravenwood "Raiders of the Lost Ark"
1981
Sigourney Weaver Ellen Ripley "Alien"
1979
Marlon Brando Don Corleone "The Godfather"
1972
Robert Redford The Sundance Kid "Butch Cassidy & the Sundance Kid"
1969
Paul Newman Butch Cassidy "Butch Cassidy & the Sundance Kid"
1969
Julie Christie Bathsheba Everdene "Far From The Madding Crowd"
1967
Terence Stamp Sergeant Troy "Far From The Madding Crowd"
1967
Alan Bates Gabriel Oak "Far From The Madding Crowd"
1967
Peter O'Toole T.E. Lawrence "Lawrence of Arabia"
1962
Anthony Perkins Norman Bates "Psycho"
1960
Charlton Heston Judah Ben Hur "Ben Hur"
1959
Max von Sydow Antonius Block "The Seventh Seal"
1957
Audrey Hepburn Princess Anne "Roman Holiday"
1953
Katharine Hepburn Rose Sayer "The African Queen"
1951
Humphrey Bogart Rick Blaine "Casablanca"
1942
Charles Laughton The Hunchback "The Hunchback of Notre Dame"
1939
Clark Gable Rhett Butler "Gone With The Wind"
1939
Erroll Flynn Robin Hood "The Adventures of Robin Hood"
1938