"Mother" by John Lennon, where he addresses the pain, sadness, and anger caused by losing both his parents. (His father left him as an infant, and his mother was killed by a drunk driver when he was 17.) He wrote two other songs about his mother: "Julia" and "My Mummy's Dead".
"Kinky Afro" by Happy Mondays. Unlike most examples of said trope in popular culture, Shaun Ryder sings it in-character, and in a rather defiant and non-apologetic way::
Son, I'm 30
I only went with your mother 'cause she's dirty
And I don't have a decent bone in me
What you get is just what you see yeah
Tyler, the Creator from OFWGKTA made a whole album called Bastard about being a literal bastard because his father abandoned him.
The Kellie Pickler song "I Wonder" is Pickler addressing her birth mother, who abandoned her.
Good Charlotte's "Emotionless" is an open letter to Joel and Benjy's father. The trope's referenced in a few of their other songs as well, including "The Young & The Hopeless" and "1979".
"Biological Didn't Bother", by NBA star and part-time rapper Shaquille O'Neal, is a diss track aimed at the biological father who abandoned him. The track ends with the words "Phil is my father", referring to his stepfather Phillip Harrison.
"11" by Cassadee Pope is about her father leaving her family when she was 11.