WOW!!, I am truely amazed that both Jay, 
as well as myself; <span style='color:gray'> actually missed this topic. </span> Boy i'm gonna have a bit of fun on this one [rubbing both hands together] 
With the exception of the first few, the rest are not necessarily in the order of favorites.
My favorite non-John Wayne movies include:
1) Decision Before Dawn w/ Richard Basehart & Oskar Werner.
2) He Walked By Night w/ Richard Basehart & Jack Webb.
3) Horatio Hornblower w/ Gregory Peck.
4) Mutiny On the Bounty w/ Clark Gable & Charles Laughton.
5) Dunkirk w/ Sir John Mills.
6) The Password Is Courage w/ Dirk Bogarde.
7) Time Limit w/ Richard Widmark & Richard Basehart.
Prisoner Of War w/ Ronald Wilson Reagan & Steve Forrest.
9) Hannible Brooks w/ Oliver Reed, Wolfgang Priess & Michael J. Pollard.
10) Stalingrad Dogs, Do you Want To Live Forever w/ Wolfgang Priess.
11) The Asphalt Jungle w/ Sterling Hayden.
12) Target Zero w/ Charles Bronson, Chuck Connors & L.Q. Jones.
13) The Dawn Patrol w/ Errol Flynn, David Niven & Basil Rathbone.
14) Seahawk w/ Errol Flynn, Olivia de Havilland & Alan Hale Sr.
15) They Died With Their Boots On w/ Errol Flynn, Olivia de Havilland & Anthony Quinn.
16) Stalag 17 w/ William Holden, Neville Brand and Otto Preminger.
17) The Great Escape w/ Steve McQueen, Charles Bronson, James Donald etc.
18) Charge of the Light Brigade w/ Errol Flynn and David Niven.
19) The Colditz Story w/ Sir John Mills, Eric Portman & Anton Differing.
20) Where Eagles Dare w/ Clint Eastwood, Richard Burton & Anton Differing.
21) Kelly's Heroes w/ Clint E, Telly Savalas, D. Sutherland & Karl-Otto Alberty.
22) The Odessa File w/ Jon Voight and Maximilian Schell.
23) The Cross of Iron w/ James Cobuer, Maximilian Schell, James Mason and Klaus Lowitsch.
24) Pork Chop Hill w/ gregory Peck & so many others.
25) Fixed Bayonets w/ Richard Basehart.
26) Star Wars w/ Mark Hamill, Harrison Ford & Sir Alec Guiness.
27) Alls Quiet on the Western Front w/ Lew Ayers and Louis Wohlheim.
28) Springfield Rifle w/ Gary Cooper, Fess Parker and Alan Hale Jr.
29) Along Came sJones w/ Gary Cooper, William Demmarrest & Dan Duryea.
30) Winchester '73 w/ James Stewart, Stephan McNally & Dan Duryea.
31) Shennandoah w/ James Stewart & Patrick Wayne.
32) Von Ryan's Express w/ Frank Sinatra and Brad Dexter.
33) Battleground w/ Van Johnson, John Hodiak and James Whitmore Sr.
34) Bataan w/ Robert Taylor and George Murphy.
35) To Hell and Back w/ Audie Leon Murphy, Charles Drake and Marshall thompson.
36) The Red Badge Of Courage w/ Audie Murphy & Bill Maulden.
37) The Bridge At Remagen w/ Robert Vaughn & Hans-Christian Blech.
38) Battle of the Bulge w/ Henry Fonda, Charles Bronson, Ty Hardin, Karl-Otto Alberty & Hans-Christian Blech.
39) Merrill's Marauders w/ Jeff Chandler, Ty Hardin & Claude Akins.
40) Pillar's of the Sky w/ Jeff Chandler.
41) The Hunters w/ Robert Mitchum & Robert Wagner.
42) Titanic w/ Richard Basehart, Robert Wagner, Clifton Webb and Barbara Stanwyck.
43) A Night To Remember w/ Kenneth More & David McCallum.
44) Battle of Britain w/ Harry Andrews, Michael Caine, Trevor Howard and Curt Jurgens.
45) The Enemy Below w/ Robert Mitchum, Kurt Jurgens & Theodor Bikel.
46) White Heat w/ James Cagney.
47) Treasure of the Sierra Madre w/ Humphrey Bogart & Tim Holt.
48) Sahara w/ Bogie, Bruce Bennett, Kurt Kreuger & Dan Duryea.
49) The Black Legion w/ Bogie.
50) Blood on the Sun w/ James Cagney.
51) The Fighting 69th w/ James Cagney & Alan Hale Sr.
52) Sergeant York w/ Gary Cooper and Walter Brennan.
53) The Unconquored w/ Gary Cooper.
54) The Last Outpost w/ Ronald Wilson Reagan, Bruce Bennett & Noah Berry jr.
55) The Savage w/ Charlton Heston.
56) Arrowhead w/ Charlton Heston, Brian Keith & Walter "Jack" Palance.
57) 55 Days at peking w/ Charlton Heston, David Niven and Harry Andrews.
58) Patton w/ George C. Scott & Karl Malden.
59) The Guns of Navarone w/ Gregory Peck & Anthony Quinn.
60) Alvarez Kelly w/ William Holden & Richard Widmark.
61) King Kong w/ Bruce Cabot & Fay Wray.
62) A Bridge Too Far w/ Michael Caine, Maximilian Schell & James Caan.
63) The Bedford Incident w/ Richard Widmark, Sidney Poitier & Eric Portman.
64) Halls of Montezuma w/ Richard Boone, Richard Widmark, Robert Wagner, Walter "Jack" Palance and Neville Brand.
65) Hell and High Water w/ Richard Widmark, Gene Evans & Cameron Mitchell.
Just to name a few.
