This is a subject with lots of potential (mwahaha). Dad pointed it out to me, which is ironic. You see, the great majority of protagonists (hero/heroine of the story) in children's literature especially, have no parents, or just one parent, or manage to get their parents out of the picture early on.
Let's start with recent hits in moviedom, primarily those drawing from books. Though I have not read or seen the story, I am under the impression that Harry Potter certainly has no contact with his parents, or has no parents at all. Frodo's parents are dead at the beginning of the Fellowship of the Ring, despite the fact that he is still considered an adolescent. Anakin Skywalker never had a father, and his mother, while playing a part in the story, is not a parental influence after the Phantom Menace. Luke Skywalker never knew his mother, and is functionally without a father. And let's not forget the Lion, the Witch, and the Wardrobe, or any of Lewis' Chronicles. The examples of children without present parents make that of Digory's mother (weakened to the point of ineffectiveness) a contrast. Cheaper by the Dozen has parents, but at least in the fictionalized movies the relationship is primarily antagonistic. And then there were a Series of Unfortunate Events...
Other children's books: Treasure Island spends its first few chapters getting away from the mother. The evil stepmother is not very motherly. Otto, of Otto of the Silver Hand, never knew his mother, and his father sends him away. The Accidental Detectives series is a marked exception, with two Christian parents at times figuring prominently in the stories. Most of the books, however, separate the characters from their parents. Frank Perretti's Cooper Kids series prominently features the strong, meek father, but the mother is dead. Little Men is about a boys' school -- no parents are present. The girl in Swan House has only one parent. There's Heidi, Naruto, the orphans in At the Back of the North Wind, the Boxcar Kids, Pollyanna, Rose in Eight Cousins, Sarah and Nellie in Little Princess, Oliver Twist, that girl in the Secret Garden, and Cosette in Les Miserables.
Now, it is reasonable and realistic for some children in stories to be orphans, as it is for some children in stories to be away from their parents. But it seems that a vast majority of children's stories include either no parents or little interaction between the parents and the children (please, correct me with examples if I am wrong). This is just a little odd!
There are several reasons I can think of for why this situation makes for a better, or easier to write story. First, the hero seems more heroic in most reader's eyes if he or she must overcome obstacles without someone else outside doing the majority of the protecting, saving, thinking, advising -- in effect, hero-ing! In addition, accurately portraying a healthy relationship (in human terms) between parents and child is difficult. A lot of people never had that relationship, so cannot write from experience. It is tempting to turn the parents into the antagonists, or into distant advisors, more the founts of wisdom than active participants in the story.
It is sad that this relationship is lacking. One might note that the father-son/daughter relationship between God and His children is also sorely lacking, even in "Christian" books. The prayer, the occasional apology, the spiritual lesson learned, is often all that can be found. What of the constant dependence, prayer and, repentance, love -- the personal relationship?
All the characters I have written into being so far are orphans, or, for the majority of the story, separated from their parents. That is not inherently wrong, but completely neglecting to write about this aspect of life can reflect a general lack of skillfulness in the author, and, more importantly, a lack of respect for the relationship between parents and children.