The hero in a film is the character that seeks something, in Casablanca is not entirely clear who this is; it is most probably Rick Blaine played by Humphrey Bogart, though it seems in parts that it could be Victor Laslo (Paul Henreid) or Isla (Ingrid Bergman). Laslo isn"t followed enough to make him the hero and Isla seems like the hero though in the end she asks Rick to make all the decisions, which puts her more in the background than you would expect the hero to be. Rick Blaine at the start of the film is really not seeking anything, which makes it less clear that he is the hero, however I think this is because the anger he feels because Isla abandoned him. It is only later, when he resolves these bitter feelings he holds within, that his goals resurface.
Major Strasser (Conrad Veidt) represents the villain, who is against the hero, but Renault (Claude Rains) at times also acts as a villain (his manipulation of women in need of a exit visa, for instance). .
The donor, who provides an object that has some magic property, is Ugati, who provides Rick with the letters of transit.
The dispatcher, who sends the hero on his way by providing a message, is hard to define, Renault kind of fills the role, as he tells Rick of Laslo's dilemma, and Rick seems impressed by Laslo, but alternatively it seems more likely to be the injustice that Rick feels the Germans are guilty of, that acts as the dispatcher.
The helper, who aids the hero, at times this is Renault, he vouches for Rick to Strasser, he goes along with Rick's plan, and he covers for him after he kills Strasser. On occasions though, Renault also acts against Rick, for example when he phones Strasser instead of the airport. Rick however had placed him in a very dangerous position at this point; so overall I would still say he was Rick's helper.
The princess, who acts as reward for the hero and as object of the villain's scheming, is physically portrayed by Isla, but the reward really seems to be that Rick is given back his faith in life and love.