Cry Me a River (1953)
A man has come crawling back to the love he rejected and she wants him to prove he is suffering as much as she did. Written by Arthur Hamilton for Ella Fitzgerald in the film Pete Kelly's Blues, it was cut in editing because the word "plebeian" sounded too communist. First and most famously recorded by Julie London in 1955 it contains one of the best rhymes in music.
Remember, I remember, all that you said
You told me love was too plebeian
Told me you were through with me 'n'
Now you say you love meWhat's New (1939)
Well, just to prove that you do
Come on and cry me a river
Originally written for Bing Crosby and recorded by several men including Frank Sinatra, I think it sounds much better in a female voice and Linda Ronstadt's 1983 recording is the best rendition.
A woman meets a former lover on the street and she tries to make small talk with him while still being deeply and painfully in love with him.
My Man (1915)
A French song, Mon Homme, made famous in Europe by Folies Bergère chanteuse Mistinguett. It crossed the Atlantic for the Ziegfeld Follies of 1921 where Fanny Brice stopped the show with her English language rendition.
Standing alone on a street corner, a woman tells of her desperate love for a man who barely care about her. He's a horrible lover, both physically and mentally abusive, but she can't help herself.
Two or three girlsWhen Barbara Streisand performed the song in the movie Funny Girl she defanged the song by cutting the line about being beaten.
That he likes as well as me
But I love him
I don't know why I should
He isn't true
He beats me, too
What can I do?
I dissed male torch songs but this one deserves mention. Basically the same story as What's New, a man meets a former lover and confesses he is devastates by the fact she does not love him. If Orbison's plaintive wailing of the word "crying" doesn't rip your heart out, then you have no soul.