Just by chance today I clicked on this song on honking duck - said to be the first one Jimmie Rodgers wrote. I think it's as good an example as I can think of of a song that treads the line between sentiment and sentimentality, and never strays over it. Here is a link to Jimmie Rodgers singing it, via Honking Duck.
And here are the words and a story about it from another site, which is very well worth visiting. (I put them in here in case it goes down or something, not to save people the trouble of going there.)
MRS. CARRIE RODGERS: A pal of Jimmie's, Sammie Williams, told his sweetheart good-bye and went to France -- to be killed in action. So before the war was over, Jimmie found time to pick out words and air to his first composition, a sentimental song.... From the first his railroad buddies liked the song, and the young fellows in Meridian who were his boon companions liked it. With banjo, guitar, uke, they hung around the all-night places or strolled the streets playing and singing Jimmie's song along with 'Sweet Adeline' and other sentimental ballads. But it was not until some ten years later that the world heard -- and approved of it. From 'My Husband, Jimmie Rodgers,' reprinted in Dorothy Horstman, Sing Your Heart Out, Country Boy, New York, NY, 1976, p. 282
This song was recorded by Jimmie Rodgers at his first ever recording session for RCA Victor's talent scout Ralph Peer at 408 State Street, Bristol, TN, 4 Aug 1927 (released as Vi 20864). © 1927 Peer International Corporation Lyrics as reprinted in Dorothy Horstman, Sing Your Heart Out, Country Boy, New York, NY, 1976, p. 282-283
The Soldier's Sweetheart
Once I had a sweetheart,
A sweetheart brave and true.
His hair was dark and curly,
His loving eyes were blue.
He told me that he loved me,
And he often proved it so.
And he often came to see me,
When the ev'ning sun was low.
But fate took him away
To this awful German war,
And when he came to say goodbye,
My heart did overflow.
He says, "Goodbye, little darling,
To France I must go."
He takes the golden finger ring
and he placed it on my hand,
Said, "Remember me, little darling,
When I'm in no man's land.
He promised he would write to me,
That promise he's kept true.
And when I read this letter, friend,
I pray the war is through.
The second letter I got from him,
The war was just ahead.
The third one, wrote by his captain,
My darling dear was dead.
I'll keep all of his letters,
I'll keep his gold ring, too.
And I'll always live a single life
For the soldier who was so true.