While I like all of the ones mentioned, there are few in the drama genre that are heart-rending yet the script, actors and director keep them from being maudlin.
The Yearling...Gregory Peck, Jane Wyman and their pre-adolescent son who is an only child, surviving in backwoods Florida after the Civil War. 1946
A Tree Grows In Brooklyn...a very poor but loving family, whose greatest desire is for the young daughter to get a good education. 1945
Make Way For Tomorrow...character actors in leading roles as an elderly couple who face an uncertain future. 1937
Remember The Night...Kindly New York Assistant DA Fred MacMurray escorts underprivileged Barbara Stanwyck to Indiana at Christmas. 1940
The Heiress...Olivia de Havilland in 1880's New York, unable to meet her father's expectations that she match her deceased mother's social graces, is romanced by Montgomery Clift, her father is suspicious of his motives, and she undergoes a transformation. 1949
Marty...Ernest Borgnine as an lovelorn Italian-American butcher who unexpectedly finds his soul mate. 1955