One of the reasons the Batman is such an excellent cartoon (forgive me I haven't read the comics nor kept up with the movies) is that the heroes and villains are equally interesting. The first Spiderman movie suffers from a weak villain and Matrix Reloaded fails in that the villain is more sympathetic than the hero, who sadly becomes one-dimensional.
Anyhow, Batman is a psychologically complex character. It is hard to get to the bottom of his true character because he puts on two masks, one as Batman and one as Bruce Wayne as compared to Robin, who is Dick Grayson regardless of the mask. As Bruce Wayne, he comes off something of a goody two shoes, a "boy scout" as Summer Gleeson observes, despite being the owner of the successful Wayne Enterprises, the corporation he inherited from his parents. As Batman, he is a crime-fighter. He will defeat villain after villain using both strength and intelligence yet won't kill them because he is so noble. Woman, such as Catwoman and Batgirl, are attracted to the mysterious Dark Knight but not to Bruce Wayne, unfortunately. As Bruce Wayne has to keep up appearances, he cannot have a real girlfriend.
A flaw in Batman's character is his desire to attain perfectionism in everything he does from martial arts to his detective skills. Convinced that his idea of justice is correct, he cannot accept other forms of justice, such as that of the sadistic guard Lock-Up. While he is very observant, it makes him overly suspicious. Even Robin is not worthy of Batman's trust. Batman has to be the greatest crime-fighter; he can't be second best and thus, Robin remains his sidekick, never his successor, something that frustrates Dick Grayson to no end. According to Batman Beyond the cartoon, he ends up bitter, giving up crime-fighter because of his old age.