Parents are supposed to the the authorities for their children, but these parents may not be good at it. They usually mean well, but when it comes to disciplining their children, they are too afraid or refuse to for any reason.
If this goes on, the kid usually turns into a Spoiled Brat/Bratty Half-Pint with bad social skills.
Obviously, Truth in Television.
If they do, infact, disipline their child, then this will lead to Was Too Hard on Him.
Can be related to Stupid Good if parents love their children too much because of it. Contrast Good Parents who love their children, but know when it's necessary to draw the line in disciplining them. Also contrast Abusive Parents where parents love punishing their children.
Compare to Extreme Doormat.
A Judge Dee fanfic uses this: a young boy with many facial tics, whose father seems completely indifferent, never beating or praising him, while his mother alternates between love and hate. It turns out the man was sterile, so his wife slept with another man to conceive (which, in eight-century China, was a horrifying crime, both the adultery and the fact that the husband did nothing against it). Ever since, the father doesn't punish the boy for fear of going too far, the mother is constantly reminded that she failed as a wife, and as a result the poor boy is growing up very confused.
The Homestuck fanfic Moirailegiance is Science mentions that Eridan's lusus actually played a role in turning him into such a Royal Brat. His parenting style was basically "Make the troll happy, and nothing works, tail-whip him,"
Charlie and the Chocolate Factory has Veruca Salt's parents, who have spoiled her rotten to the point that her father would rather just buy her whatever she wants no matter how outrageous just so he won't have to put up with her tantrums. It is shown at the end of the 2005 film adaptation that Mr. Salt does learn to say "no" to her though, subverting this ultimately.
Live Action TV
Shown many times in Maury with violent teenage girls, with parents (usually only moms) who are terrified of their daughters, and are afraid of disciplining them.
The Bible: Various passages from the Book of Proverbs, Proverbs 13:24 particularly, mention that parents who withhold themselves from disciplining their children are the ones who don't love them.
In one episode of The Adventures of Jimmy Neutron: Boy Genius, there was rich father who didn't want to discipline his snobby son, Eustace Strytch, for his behavior because he was too ashamed. At the end, after Hugh gives him tips, he finally disciplines Eustace by punishing him for a month.
It's implied that this doesn't stick later as in the second episode that features Eustace, Jimmy makes a callback to the father having grounded him, only for Eustace to reply, "My father's will is easily manipulated."
Only to Sarah, mind you. Ed is infamously grounded in one episode, and his parents remove the stairs to ensure he can't escape.
Edd: That's disturbing.
Vicky's parents in The Fairly Oddparents are downright terrified of Vicky, and they are afraid of disciplining her.
A Johnny Bravo episode has him baby sit a kid with magic powers (a parody of Timothy from It's a Good Life). The parents are afraid of the kid big time, so they let him do what he wants.
An implied zig-zagged example of The Powerpuff Girls is with Daddy Morebucks, Princess Morebucks' father. It's shown that he rarely disciplines his daughter when she throws temper tantrums, and gives her money to get her silenced. The ending of an episode when Princess becomes the mayor also implies that he gives her proper discipline when necessary.
Charlotte and Drew Pickles towards Angelica sometimes in Rugrats.
In the The Simpsons episode, "The Itchy and Scratchy Movie", during a parent-teacher conference, Marge explains to Mrs. Krabappel that she and Homer have a hard time disciplining Bart whenever he does something wrong and are encouraged by her to start being firm about it. Following her advice, they get better at disciplining him, such as when they send him to bed without dinner for breaking Grandpa's teeth, and preventing him from seeing The Itchy and Scratchy Movie when he doesn't watch Maggie and she drives Homer's car.
In a Flashback on The Simpsons it's shown that Ned Flanders' parents were beatnicks who didn't believe in punishing their son for his unruly behavior, but on the other hand didn't want the behavior to continue.
Dr. Foster: Would you please tell your son to stop [tearing my office apart]?
Ned's Dad: We can't do it, man! That's discipline! That's like tellin' Gene Krupa not to go "boom boom bam bam bam, boom boom bam bam bam, boom boom boom bam ba ba ba ba, da boo boo tss!" We don't believe in rules, like, we gave them up when we started livin' like freaky beatniks!
Dr. Foster: You don't believe in rules, yet you want to control Ned's anger.
Ned's Mom: Yeah. You gotta help us, Doc. We've tried nothin' and we're all out of ideas.
Liane Cartman from South Park admits that she doesn't give Eric any discipline because she is insecure about not having any friends.
On Gravity Falls, Gideon's parents do nothing to curb his behavior. His dad Bud is a pretty laid back guy who usually goes along with whatever Gideon's planning, while his mother is practically catatonic, only ever seen vacuuming. In fairness to them, Gideon is a complete psychopath, and is probably responisble for his mother being in such a state in the first place.