Batman: Batman's children

True, Batman is a father. In fact he has fathered more than one child. Officially Bruce Wayne is still a millionaire playboy that has remained single and has no children, but that's Bruce. Batman is another story. It all began in a graphic novel called Batman: Son of the Demon where Batman faced one of his most intriguing foes, a man called Ra's al ghul (the same of Batman Begins). Ra is a terrorist of sorts that believes the planet faces a great threat and that threat is called mankind. So in other words Ra has assumed the task to save the planet but once and again "The Detective" as he calls Batman has stopped him. Ra is a difficult adversary for many reasons: he has a lot of followers and wealth is not a problem either besides he has The Lazarus Pit which is a special pool that can rejuvenate individuals and  even resurrect the Dead. More importantly Ra knows Batman's secret identity. To make matters worse Ra has a dauhter called Thalia who happens to be attracted by Bruce but also believes in her father's "cause". As usual Batman manages to defeat Ra against imposssible odds, but something happens at the end of this story, something completely unexpected: Bruce and Thalia decide to play Midnight Olympic Games. For once the always careful hero gives in to his own desires and there is a result reveled in the final panel, a baby boy apparently given in adoption. For years this story was considered non-canon meaning that it happene outside the regular continuity of Batman, but one day they decided to use the baby and introduced him to his father. His name is Damian and he has been trained to be the heir of Ra's empire if he ever decided to stop rejuvenating himself. Eventually Damian ends up at his father side and yes, he is at this point the new Robin.
Update (May 1st, 2013): This last line is no longer true since Damian  is, at least at the moment, dead after facing Leviathan, a clone of himself also genetically enhanced to look older and a lot stronger)

Damian is not Batman's first child. In a parallel universe a Batman that is older than ours has married Selina Kyle (Catwoman) and they had a daughter who also decides to don a costume with a name of her own: The Huntress. Since what happens in that universe is usually mirrored by ours it is believed that someday Bruce and Selina will tie the knot and have a daughter, the Huntress of this universe. The Huntress once appeared in her own TV series , a short-lived one, along the daughter of another superheroine, Black Canary. In the series Batman is nowhere to be found after a final encounter with the Joker so it is up to Daddy's little girl to take care of Gotham City. In this series she is mentored by none other than Barbara Gordon when she is no loger Batgirl but Oracle, the identity that Barbara adopted after being shot by the Joker, shocking event that left her crippled for life. The Huntress managed to appear with Batman without being his daughter but that of a mobster. Craving for justice Helena Bertinelli (her name in this reality) adopted the mantle of The Huntress and patroled Gotham with the reluctant acceptance of Batman who was a little displeased by her somewhat violent methods.

Yet, in another continuity, a future continuity, there is a Batman that had his own series, Batman Beyond, which tells the stories of one Terry Mc Ginnis, a young man who is trained by an aged Bruce Wayne to be the next Batman now wearing a more advanced version of the Batman suit fighting new foes in the Gotham of the future. In the series their true relation is never revealed because both were unaware of that. It is much later in one of the chapters of the Justice League Unlimited series where we get to know that by thanks to Amanda Waller's machinations (Amanda is the FBI and the CIA in one person) the genetic makeup of Mr. Wayne had been infused in the body of Terry's father making him an unwilling vehicle for the reproduction of yet another Son of the Bat which explais why both Bruce and Terry in spite of having a tense relationship they work together pretty nicely.
For a man who is so careful about his actions and does not want to risk the life of those dear to him, Mr. Wayne seems to be very resourceful in finding ways to become a Daddy anyway. Personally I have found in this character a tremendous desire to be a parent. That ahould be the explanation for all those colorful Robins that he has allowed to fly around him so often and so many times.