All-Loving Hero: The voice of peace between the humans of Iron Town and the animals/spirits/deities of the forest. Without him the movie would have been much shorter and very bloody.
Archer Archetype: While a skilled swordsman, his truly badass feats are performed with his bow. He also proves himself perfectly capable of living alone in the wilderness without other people.
Bad Ass Normal: Even before receiving the curse, Ashitaka manages to kill an enormous boar demon singlehandedly.
Better as Friends: Zig-Zagged. While San does come to reciprocate his feelings, at the end, they realize that neither of them could give up their present life styles for each other, and the two part, promising to still meet each other every so often.
Big Brother Instinct: During the demon attack at the beginning of the film, Ashitaka the pacifist is initially very reluctant to attack and spends quite a while trying to pacify Nago. When he sees the demon boar charging towards Kaya, however, he doesn't hesitate to shoot it square in the eye.
Love at First Sight: Towards San. He gets that "awe struck" look in his eye and calls her "beautiful" when they speak to each other for the firs time.
Mark of the Beast: His curse manifests as a large, nasty scar which starts on his arm and spreads throughout his body.
Martial Pacifist: Ashitaka is a pacifist in a world where humans and nature are at war. The funny thing is Ashitaka actually aims to be a Badass Pacifist, but what keeps him from reaching that is the fact that he will kill you if you leave him no other choice.
Memento Macguffin: The crystal necklace that he gets from Kaya for good luck and so he won't forget her. He later gives it to the wolves, as a token for San.
Better as Friends: Zig-Zagged. While San does come to reciprocate Ashitaka's feelings, at the end, they realize that neither of them could give up their present life styles for each other, and the two part, promising to still meet each other every so often.
Boomerang Bigot: Hates humans even though she is one. Justified given how she was raised by her adoptive wolf family from infancy because her parents left her to be eaten by them.
Red Baron: "Mononoke Hime" means "the princess of vengeful spirits". Not knowing her real name, the villagers call San "Princess Mononoke" out of fear.
Red Is Heroic: The red fang markings. Although, she's more of an anti-hero: While Lady Eboshi and her followers are desecrating the forest and the spirits, San's method of murdering them all isn't exactly a great solution.
Tsundere: Has elements of it. For example, when Moro comments that Ashitaka wanted to share his life with her, San angrily responds that she hates him like she hates all humans. A few seconds, one of her brothers comes to give her a necklace from Ashitaka. San puts it on.
Anti-Villain: She is overall a rather considerate leader, kind to lepers, prostitutes and the disenfranchised and has her town's best interests at heart. Her violence, arrogance and antagonism are rather understandable when you consider how she is being proverbially roasted by wild animal gods on one end and by other warlords on the other.
Eboshi: Now watch closely, everyone. I'm going to show you how to kill a god. A god of life and death. The trick is not to fear him.
Badass Normal: Able to buy up the bond of every brothel girl she meets and gives them a new and better life in Irontown. Also, she kills gods.
Big Good / Big Bad: Depending on your point of view in the film's Grey and Grey Morality. Lady Eboshi generally cares for the people of Irontown and they in turn look to her as beacon of hope as sorts. But, she's also the one after the Forest Spirit.
Face Death with Dignity: In sharp contrast to Nago and later Okkoto, who went insane and turned into a demon after being shot by a poisoned bullet, Moro is calm and accepting of her inevitable demise. Even when San begs her to go to the Forest Spirit to be healed of the bullet wound, Moro replies that she's lived long enough.
Big Good / Big Bad: All depending on your point of view within the movie's Grey and Grey Morality. For the former, the Forest Spirit is beloved by all and seen as a sort of guardian. However, if you shoot his head off, he'll quickly become the latter.