It's hard to imagine a better literary example of the perfect single father than Atticus Finch in the novel To Kill a Mockingbird. Atticus is left to bring up his children alone after his young wife died of a sudden heart attack. Although Atticus is much older than most of Jem and Scout's friends, it is his wisdom that helps to guide his children through life in tiny Maycomb. He always finds time each day to read with Scout, and when the kids need to have a heart-to-heart talk, he makes himself available.
He gives the children more independence than most parents, and they respond by trying to make him proud of them. When Jem makes the seemingly reckless decision to return to the Radley House to retrieve his lost pants, he tells Scout
"Atticus ain't ever whipped me since I can remember. I wanta keep it that way."
Jem does not fear a whipping (Atticus apparently has never spanked either of them); he just doesn't want to disappoint Atticus. He allows them to watch the remainder of the rape trial (after sneaking in and being discovered) despite the ire of Alexandra and Calpurnia.
Atticus always speaks the truth with Jem and Scout, telling his brother, Jack,
"When a child asks you something, answer him, for goodness' sake... they can spot an evasion quicker than adults."
He allows them the freedom to curse once in a while, but he cautions them about using the word "nigger." It's "common," he tells Scout. He debates his sister, Alexandra, about the wisdom of making Scout more lady-like, allowing her to wear her beloved overalls constantly. In the end, the children turn out okay. We know this from the first pages of the novel, when the grown-up Scout seeks out a much older Atticus for advice--just as she had when they were children. The diplomatic but straight-shooting Atticus "said we were both right."
Atticus's function is to contrast the popular opinion and attitudes of Maycomb at the time of the novel. He is also the moral center of the novel. He does what no one is really willing to do—defend an innocent black man who has been accused of rape. The majority of the people would just let the mob mentality lynch Tom and southern justice would reign supreme. But Atticus doesn't let that happen.
There are numerous examples of this. He stands up to the lynch mob that comes to get Tom. Jem reads cartoons about Atticus in the paper depicting him as a dull, hardworking legislator. Scout sees her father bravely and heroically kill a rabid dog and then shrug off all credit for it. And Atticus is the one who constantly tells Scout not to judge others until she has put herself in their situation.
It is little wonder that several years ago TBS rated Atticus as the greatest hero ever depicted on the silver screen (from the film adaptation of the novel). I think it's safe to say there everyone can find something heroic and redeemable in Atticus's character.
Comparing him to most fathers is really unfair. Outside of treating his children like adults, it's hard to find fault with Atticus. Most fathers, I think, would have some of Atticus's characteristics, but I find it hard to imagine that most fathers can really "walk the walk and talk the talk" in terms of his morals and ethics as Atticus does.