In the book it was stated that she had a long pointed chin, a rather mannish jaw, and Fiyero commented that she seemed to have a strange scar near her genitals. And that was before she went utterly insane and stopped sleeping all together, she probably looked like hell by then. Despite this, there are still indications that she's still rather good-looking, in an unconventional way — her nose, while strong, is described as lovely, and both Galinda and Fiyero tell her she's pretty at separate points. Galinda even goes on about Elphaba's beautiful hair, and says that there's an "exotic" type of beauty about her after a mini-makeover. Elpahaba is described as looking like her mom, but with green skin, at least once in the books.
In the musical, she only calls Elphaba pretty after "Popular", after she's Galinda-fied her with a flower and better hairstyling. Fiyero in the book refers to her as being "beautiful in her own way", meaning she's not conventionally attractive, and in the musical he finds her beautiful because he's "looking at things differently", which can be taken in multiple ways. The makeup designer flat-out stats that "Elphaba is not ugly — she's supposed to be beautiful. People just hate her because she's green." Notably, her ensemble changes entirely for the latter part of the play, as she drops the bulky boots, glasses and drab school outfit and switches to a sexy black gown instead.
Child by Rape: In the book, at least. In the musical, it could be interpreted as both parts getting drunk.
Dark Is Not Evil: She may wear black, have black hair, and seem Gothic, but she cares about her sister, animals, and her anthropomorphic teacher and desperately wants to do good. This eventually leads to her Villainous Breakdown.
Hermaphrodite: Book Elphaba is strongly implied to be at least mildly intersex. Besides her "mannish" features, she occasionally seems to get a little confused about what equipment her body is "supposed" to have.
Not Good with People: Type two. She is very snarky, has a hard time expressing her feelings and seems to get along much better with Animals and animals.
Reality Warper: Implied, discussed and exhibited on one occasion. She seems to be able to make things happen unconsciously, without even thinking them.
Rebellious Spirit: In the book, she's almost rebellious for the sake of it — she insults almost everybody. In the musical, she becomes this once she meets the Wizard and realizes the depth of his corruption, declaring "I'm through with playing by the rules of someone else's game." and "I'm through accepting limits 'cause someone says they're so / Some things I cannot change, but till I try I'll never know!" She then begins her "campaign of terror."
Seer: Has this power in the musical; she predicts the fact that there will be a celebration all to do with her. (though she doesn't predict that said celebration will be her funeral.) She also sees her sister's death.
The Snark Knight: Eventually, in the musical. She's sarcastic and introverted from the start, but at first, she has an idealistic streak ("The Wizard and I") - after "Defying Gravity", she evolves into a genuine, cynical Snark Knight.
The Unfavorite: In both book and musical, her father heavily prefers Nessarose.
Villain Protagonist: Not in the musical, but the book has her genuinely going insane from all the failures of her life, making her into a very malevolent being by the time Dorothy shows up. She stops sleeping entirely, stalks Dorothy, kills a woman, threatens her former friends and when Dorothy and co. finally get to her castle, she's fallen into utter desperation. Very sympathetic, yes, but still quite villainous.
Voice Types: Is a classic, prime example of a mezzo-soprano "Belter". Most Elphaba actresses in the musicals are graded (by the fans) on the quality of: the end notes of "The Wizard and I", the long "Fi-yer-o-o-o-o-o!" in "No Good Deed Goes Unpunished, and the end of "Defying Gravity", particularly the final line and the last belted "Ah-aah-ahhhh!"
Well-Intentioned Extremist: Book-verse, Fiyero calls her out on it. She's okay if "accidents" happen when trying to make her point.
Book Dumb: At least, compared to Elphaba. More so in the musical than in the books.
Character Development: In the book Galinda starts of as rather vapid and shallow. But after meeting Elphaba, along with Dillamond's death, she realizes there's much more important things to worry about besides boys and popularity.
The Ditz: In the musical. In the books, she's actually very intelligent and capable.
Genki Girl: In the musical, especially during the "Popular" and "One Short Day" scenes.
Inept Mage: Early on she qualifies. She gets better. She's the only one of the girls who actually has a formal education in magic in the books, and is not capable of doing many impressive things with it, though by the standards of Ozian society, she is actually very talented(In the sense that she doesn't accidentally set things on fire).
Large Ham: The role practically calls out for this, especially compared to the more dour and sarcastic Elphaba. The song "Popular" is often the benchmark for any actress playing G(a)linda, as it involves a lot of hopping around, dancing, yodelling, and often bits of improvised comedy unique to that actress. Most later actresses took Kristin Chenoweth's performance and built on it, creating a series of zanier Glindas.
Light Is Not Good: Partially subverted later. She may be pretty and popular, but she is vain and too dumb to realize what the Wizard had done. She redeems herself in the end.
Stepford Smiler: Indicated in the novel Wicked, developed in the sequel, Son of a Witch. The musical makes her a Stepford Smiler at the behest of the state for the sake of keeping the populace blissfully unaware.
That Woman Is Dead: Borderline parody when she changes her name from Galinda to Glinda in the play. Played much more sympathetically in the book.
Voice Types: A soprano — the role in the musical was written for Kristin Chenoweth. Many notes were added (at her request) to the opening number just so she could hit some high notes.
Word of Gay: From the author and original cast. The book barely tries to hide it when the cuddle together "for protection".
It helps that she married for money in the book. Though she did genuinely care for him, she had no romantic love for her late husband.
"You're going to lose your heart to me, I tell you! Even if I have to...I have to...magic spell you!!!"
Cruel Mercy: In the book a Munchkin asks her to enchant a woodsman's ax so that it would kill him when he swings it. She said this would be cruel, so instead she enchants it so it simply cuts off his limbs. And thus the tin woodsman is born.
Disabled Love Interest: In the musical she was a lovely young girl in a wheelchair. Less so in the book, where she was a zealous girl who had functioning legs, but no arms to speak of, which puts a damper on finding love.
Yandere, at least in the musical, where she is willing to strip the Munchkins of their rights and keep any of them from leaving the country just to keep Boq with her and then curse away his heart when he expresses the desire to leave.
Adaptation Distillation: He has a whole portion of the book devoted to him, yet is at-best a side character in the musical — he doesn't even get a whole song to himself, just small bits of other people's songs.
Adorkable: Especially around Glinda. Then he's turned into the Tin Man...
All Love Is Unrequited: Musical only. He loves Galinda, who won't give him the time of day. Nessarose is absolutely smitten with him, but he doesn't feel much more than sympathy for her, which decreases rapidly as time goes on.
Dogged Nice Guy: In the book he pursued Galinda for quite a while during his time in school. But eventually she set the record straight that it would never work out, and he gave up when she became more serious, and he grew up a bit.
The Everyman: In the book, he's a defining "this is what normal people are like" character, compared to the snobby Galinda (and her friends), sullen and sarcastic Elphaba, and whacky frat boys Avaric, Crope and Tibbett.
Flanderization: His crush on Galinda he has for a summer or two in college becomes the defining character trait his whole life in the musical.
Happily Married: In the book he winds up living a happy, yet mundane, life as a farmer, father, and husband.
Stalker with a Crush: In the musical — Glinda's clearly not interested, and he still wants to break up her engagement years after they leave school.
Arranged Marriage: In the book he is arranged to be married when he is in Shiz. He ends up marrying her and having three children with his wife. That doesn't seem to stop him from having some "fun" with Elphaba in the Emerald City, as it's generally a loveless union.
Composite Character: In the Musical he's a mix of Book Fiyero (with his name and position of Prince), while his personality is more along the lines of Avaric (and possibly Crope and Tibbett) taken Up to Eleven
Satellite Character: Despite mattering heavily into the plots of both book and musical (indeed; most of either story would have never happened without him), he actually doesn't appear a whole lot, and instead revolves around Elphaba. Characters spend more time talking about him in absentia in the book, and he's only in one song in the play, and three scenes altogether.
Verbal Tic: A truly disturbing instance in the musical.
What Do You Mean, It's Not Symbolic?: In the book Boq is fascinated that "Dorothy" means "gift of the gods" and the ruler (president) of her land at the time was named "Theodore", which means "God of gifts".
Bi the Way: He is in the center of a Love Triangle with a man and a woman. Who may have fallen in love with each other, too, or died separately.
In book four, it's revealed that neither one died, and if they met they didn't hit it off. Liir ended up married to Candle because she was the mother of his daughter, but still in love with Trism although they didn't see each other for years. (This might make him Ambiguously Gay, since while he seems to have regular sex with his wife they don't have much of a romantic attraction, something he and Trism enjoy in spades.) In the end, when Candle and Trism both leave him, he tells Rain he'd be happy if either or both of them would just come back.
That said, he certainly accomplishes quite a lot more than his mother, including missions he inherited from her failures.
Progressively Prettier: He is described as being fat in the first book, but second book onwards has him losing the weight and becoming lean, pale and dark-haired. Possibly justified in that he spent some time in the army and may have gotten into better shape during that time.
Character Development: Bordering on Dynamic Character. He is very different in all periods of his life from what he was at the start of his life, through his journey with Dorothy, integration with human society, etc. etc. All this from a character who doesn't really move the plotline at all. Although he ends the novels as ruler of Oz
Who Is This Guy Again?: He was only mentioned a handful of times in the first book, and completely cut out of the musical. Causing lots of people reading the second book to double take when remembering that yes, Elphaba had a brother.