The main character in Carrie Underwood's "Blown Away" is heavily implied to have been abused by her alcoholic father.
Disturbed's "Down With The Sickness".
John Michael Montgomery's "The Little Girl," where the title character witnesses her father beating her mother ... and then one day witnessing his murdering her before turning the gun on himself.
"Kristy, Are You Doing Okay?" by The Offspring. The song is meant to be an apology to a girl that lead singer Dexter Holland, as well as his friends, knew was sexually abused during her youth by her father, yet no one ever brought it up.
"Amy in the White Coat" by Bright Eyes is about the life of a girl who is being sexually abused by her father. The song is told through the point-of-view of her father, and some of* her classmates.
"Janie's Got a Gun" by Aerosmith is about a girl who murders her father because he sexually abused her.
Take a song by Korn. Any song. Usually it's more about neglect than direct abuse, but to the children in the songs, it feels just the same.
Regal Pinion has a song called "For the Best" is about a daughter at her abusive father's funeral. His actions range from locking her in her room for hours on end to telling teacher's she "bumped into the chair". Regal has stated that he wrote the song as a Take That to people who ignored the signs but did nothing of it.
Teachers saw her as that god damn "one kid" / The one you fantasize in mind's eye you'd rid
"Oh if only I knew then I'd do something different." / Well you did nothing, so congratulations
Voltaire's song "The Chosen". The protagonist says "First time I had sex I was three/ First time consenting was thirteen", and claims that his mother "once left me in a supermarket".
Alanis Morissette's "Perfect" is about parents who live vicariously through their kids and humiliate and berate them for not meeting expectations.
We love you just the way you are / If you're perfect.
Referenced near the end of the Pink Floyd song "Dogs"
Pat Benatar's "Hell is for Children", about the utter hell that kids with abusive parents have to live through:
"Be a good boy and you'll get a new toy/Tell Grandma you fell off the swing."
Invisible Circles by After Forever is a Concept Album centered on this theme, inspired by some of the children guitarist/vocalist Sander Gommans encountered during his previous job as an art teacher. In this story, the workaholic father refuses to compromise his chances at his dream career to help raise his daughter, leaving the mother to give up her job completely to spend time with the girl. This progresses for several years with the father rarely around and the mother taking out her frustrations on the daughter, who retreats into an escapist fantasy online in search of positive attention she doesn't get at home. But things go From Bad to Worse when an argument ends with the father walking out on both of them...
"Prison Sex" by Tool
Quite a few songs by The Mountain Goats, due to John having been abused himself. The entire album "The Sunset Tree" was about his abusive stepfather, particularly "Dance Music" and "This Year". A special note also goes to the soul-shattering "Song for my Stepfather".
Not quite Played for Drama, but definitely present in "Amos Moses" by Jerry Reed. Amos' surly demeanor is explained by Amos's father using him to bait alligators while hunting when Amos was a child. This, err hands-on approach to gator hunting at one point cost Amos his entire left arm up to the elbow.
Although the parents in Tommy appear to mean well, they take Parental Neglect so far that it's a matter of opinion whether it amounts to this. Their attempts to cure their son include paying a gypsy to feed him acid. They are also known for leaving him alone with his abusive cousin and/or his drunk rapist uncle. According to Word of God re: an early interview with Pete Townshend, Tommy's dad hits him for being deaf, dumb and blind (never mind that his own actions—killing a man in front of Tommy and then forcing him to keep quiet—actually traumatized the poor kid enough to have caused these disabilities in the first place). While it's perhaps not intentional, the way both parents refer to him simply as "the boy" comes off as fairly sociopathic.
TenThousandManiacs"What's the Matter Here?" addresses the issue of neighbors abusing their child, and the protagonist wanting to act, but not daring to intervene:
"If I'm the only witness to your madness offer me some words to balance out what I see and what I hear. All these cold and rude things that you do I suppose you do BECAUSE he belongs to you,and instead of love, and the feel of warmth you've given him these cuts and sores that don't heal with time or with age."
Skillet has a few songs reflecting Cooper's relationship with his father. He says his father wasn't physically abusive like "Open Wounds" suggests, but he was emotionally abusive. All of the songs involving Cooper's relationship were written and performed by him.
"Little Bird" by Imogen Heap seems to be about this trope, although it could also be spousal abuse. Either way, the narrator of the song gradually discovers the abuse and asks the little bird of the song's title to help rescue the victim, only for the little bird to abandon them at the end of the song.