| | 1937 | THE HURRICANE | Best Music (Score) Nomination |
| 1937 | THE PRISONER OF ZENDA | Best Music (Score) Nomination |
 | 1938 | ALEXANDER'S RAGTIME BAND | Best Music (Scoring) Oscar |
| 1938 | THE GOLDWYN FOLLIES | Best Music (Scoring) Nomination |
| 1938 | THE COWBOY AND THE LADY | Best Music (Original Score) Nomination |
| 1939 | THE HUNCHBACK OF NOTRE DAME | Best Music (Scoring) Nomination |
| 1939 | THEY SHALL HAVE MUSIC | Best Music (Scoring) Nomination |
| 1939 | THE RAINS CAME | Best Music (Original Score) Nomination |
| 1939 | WUTHERING HEIGHTS | Best Music (Original Score) Nomination |
| 1940 | THE MARK OF ZORRA | Best Music (Original Score) Nomination |
 | 1940 | TIN PAN ALLEY | Best Music (Score) Oscar |
| 1941 | HOW GREEN WAS MY VALLEY | Best Music (Scoring of a Dramatic Picture) Nomination |
| 1941 | BALL OF FIRE | Best Music (Scoring of a Dramatic Picture) Nomination |
| 1942 | MY GAL SAL | Best Music (Scoring of a Musical Picture) Nomination |
| 1942 | THE BLACK SWAN | Best Music (Scoring of a Dramatic or Comedy Picture) Nomination |
| 1943 | CONEY ISLAND | Best Music (Scoring of a Musical Picture) Nomination |
 | 1943 | THE SONG OF BERNADETTE | Best Music (Scoring of a Dramatic or Comedy Picture) Oscar |
| 1944 | IRISH EYES ARE SMILING | Best Music (Scoring of a Musical Picture) Nomination |
| 1944 | WILSON | Best Music (Scoring of a Dramatic or Comedy Picture) Nomination |
| 1945 | STATE FAIR | Best Music (Scoring of a Musical Picture) Nomination (shared with Charles Henderson) |
| 1945 | THE KEYS OF THE KINGDOM (1944)* | Best Music (Scoring of a Dramatic or Comedy Picture) Nomination |
| 1946 | CENTENNIAL SUMMER | Best Music (Scoring of a Musical Picture) Nomination |
| 1947 | CAPTAIN FROM CASTILLE | Best Music (Scoring of a Dramatic or Comedy Picture) Nomination |
 | 1947 | MOTHER WORE TIGHTS | Best Music (Scoring of a Musical Picture) Oscar |
| 1948 | THE SNAKE PIT | Best Music (Scoring of a Dramatic or Comedy Picture) Nomination |
| 1948 | WHEN MY BABY SMILES AT ME | Best Music (Scoring of a Musical Picture) Nomination |
| 1949 | COME TO THE STABLE | Best Music (Song) Nomination (shared with Mack Gordon) For the song "Through a Long and Sleepless Night" |
| 1950 | ALL ABOUT EVE | Best Music (Scoring of a Dramatic or Comedy Picture) Nomination |
| 1951 | DAVID AND BATHSHEBA | Best Music (Scoring of a Dramatic or Comedy Picture) Nomination |
| 1951 | ON THE RIVIERA | Best Music (Scoring of a Musical Picture) Nomination |
 | 1952 | WITH A SONG IN MY HEART | Best Music (Scoring of a Musical Picture) Oscar |
 | 1953 | CALL ME MADAM | Best Music (Scoring of a Musical Picture) Oscar |
| 1954 | THERE'S NO BUSINESS LIKE SHOW BUSINESS | Best Music (Scoring of a Musical Picture) Nomination (shared with Lionel Newman) |
 | 1955 | LOVE IS A MANY SPLENDORED THING | Best Music (Scoring of a Dramatic or Comedy Picture) Oscar |
| 1955 | DADDY LONG LEGS | Best Music (Scoring of a Musical Picture) Nomination |
 | 1956 | THE KING AND I | Best Music (Scoring of a Musical Picture) Oscar (shared with Ken Darby) |
| 1956 | ANASTASIA | Best Music (Scoring of a Dramatic or Comedy Picture) Nomination |
| 1958 | SOUTH PACIFIC | Best Music (Scoring of a Musical Picture) Nomination (shared with Ken Darby) |
| 1959 | THE BEST OF EVERYTHING | Best Music (Song) Nomination (shared with Sammy Cahn) For the song "The Best of Everything" |
| 1959 | THE DIARY OF ANNE FRANK | Best Music (Scoring of a Dramatic or Comedy Picture) Nomination |
| 1961 | THE FLOWER DRUM SONG | Best Music (Scoring of a Musical Picture) Nomination (shared with Ken Darby) |
| 1963 | HOW THE WEST WAS WON (1962)** | Best Music (Score - Substantially Original) Nomination (shared with Ken Darby) |
| 1965 | THE GREATEST STORY EVER TOLD | Best Music (Score - Substantially Original) Nomination |
 | 1967 | CAMELOT | Best Music (Scoring of Music, Adaptation or Treatment) Oscar (shared with Ken Darby) |
| 1970 | AIRPORT | Best Music (Original Score) Nomination |