Abusive Parents: Anne's guardians prior to Matthew and Marilla used Anne to look after their own children, neglected her education, and did not always provide her (and possibly their own children) with enough to eat. One of these guardians, Mr. Thomas, was frequently intoxicated and Anne was exposed to his violent behaviour.
Berserk Button: Anne is initially very sensitive about her red hair, and retains a certain grudge against fate for giving it to her well into adulthood.
Blithe Spirit: Free-spirited and cheerful, in contrast to the traditionalist people of Avonlea.
Bookworm: Very fond of books. In the first book she even starts a book club.
Drama Queen: Especially in the first book, where she goes through a fiery preteen angst phase about wanting to float down the river ala Elaine, and imagining she had dark hair and was named Cordelia Fitzgerald.
Fiery Redhead: Justified since her temper was at its fieriest when she was teased about her red hair (being one of the few characters whose fire is connected to their coloring). She chewed out the neighborhood busybody (big mistake...), and also responded to being called "Carrots" by breaking her slate over a schoolmate's head.
First Love: To Gilbert, he might have dated other girls but in the end always ended up loving (and marrying!) his first crush.
Friendless Background: Anne had one prior to coming to Green Gables, leading her to create two imaginary friends.
Giant Poofy Sleeves: She desperately wants them in the first book — understandably, given the fashion was then at its height. Being able to get your shoulders through a door without turning sideways marked a woman as hopelessly dowdy. In later books, after the fashion has changed, she admits a lingering fondness.
Happily Adopted: She instantly takes to Matthew and Marilla, and loves them as if they were her real parents.
I Am Not Pretty: In the first book she's justified in thinking so, since she really is homely by the standards of her day. Her later belief that she's still not pretty, even when she's grown more attractive with age, mostly stems from how teased she was as a child.
In Harmony with Nature: Anne has elements of this — she asserts she would never be happy in a place without trees.
Redheads Are Uncool: Anne is a very cheerful person, but at times could get very careless and cause mishaps. Her relationships with the people of Avonlea began unusually friendly or openly hostile because they teased her about her red hair, which she hoped would some day darken into a real handsome auburn.
"How perfectly lovely!" exclaimed Anne, her gray eyes lighting up until they looked like evening stars, causing Mrs. Lynde to wonder anew if she would ever get it settled to her satisfaction whether Anne Shirley were really a pretty girl or not.
Good Parents: One major subplot in the first book is Marilla becoming this. In fact, when Anne nearly gets herself killed late in the first book, it's made clear that Marilla has truly come to love the girl.
Does Not Like Men: And is not shy about saying so. Captain Jim is the only man she's never said a bad word about, which he claims worries him: it makes him wonder if there's something unnatural about him.
Jerk with a Heart of Gold: She's not so much a jerk as very, very blunt. As Captain Jim says, "She's got the bitterest tongue and the kindest heart in Four Winds."
James "Captain Jim" Boyd
The Captain: While he's a retired sea captain, he still fulfills many aspects of the trope.