Foil: With Big Daddy. Both of them are charming, manipulative, self-made people who grew up poor and work hard to get what they want. It's why they earn each other's respect.
Gold Digger: Subverted, because Maggie is actually in love with Brick. But money is also important to her because she grew up poor and really doesn't want to be poor again.
Head-Turning Beauty: Alludes to being one (nearly by the trope name) in her first-act speeches to Brick- and likely true, given her MsFanservice status. However, given the play's limited cast involves two married men and her indifferent husband, we don't see this trope in action much.
Like Parent, Like Spouse: A tragic example. Maggie's father was an alcoholic who took advantage of his wife's hard work and generosity. The situation reflects Maggie's own.
Love Martyr: Invoked half-sarcastically: she calls her situation with Brick "The Martyrdom of Saint Maggie".
Ambiguously Bi: At one point, he and Maggie had a healthy, loving relationship. There's also some heavy implications he may have harbored romantic feelings for his best friend, Skipper.
Beauty Is Bad: Brick's good looks are alluded to by nearly every character in the play. He's also bitter, brutally honest, and antagonistic.
Brutal Honesty: He's incredibly up-front with Maggie about where she stands with him, and is disgusted with lies and falsehoods. He is also the one to tell Big Daddy about his cancer... albeit half by accident.
Brick: It's like a switch, clickin' off in my head. Turns the hot light off and the cool one on, and all of a sudden there's peace.
Hunk: A former football star who has kept his good looks despite turning to drink. It's lampshaded by Maggie when she remarks that most men become uglier when they start drinking, but somehow Brick looks even better than before.
Big Eater: He loves traditional Southern cuisine, and helps himself to massive portions during his birthday party.
Brutal Honesty: He lacks the manners and tact that might have been taught in school, instead outright telling people what he thinks of them and using coarse language to voice his thoughts, whatever they may be. Fitting, as he's "new money" who came from nothing.
Child Hater: A variation—he is far more interested in the idea of having children than actually dealing with them. When Mae repeatedly has her kids perform tricks and sing songs at his birthday party, he's more annoyed than entertained and snaps "Don't we ever get an intermission?"
Dirty Old Man: Maggie notes that he shamelessly admires her figure. In the film version, after being duped into thinking that his cancer test came back negative, he quite literally salivates as he describes what he plans to do:
Big Daddy: You know what I'm contemplatin' now? Pleasure. I'm gonna pick me a choice woman, and I'm gonna smother her in minks, and choke her with diamonds. Yessir, I'm gonna have me a ball.
Everyone Calls Him "Barkeep": His given name, Harvey, is almost never spoken in the play, and everyone, from his employees to his children to his own wife, calls him "Big Daddy." The latter is especially painful: though everyone else refers to her as "Big Mama", Big Daddy only uses "Ida" when talking to her, suggesting that he doesn't see her as his equal.
Fiction 500: He has ten million dollars in cash and "blue chip," or expensive, stock, as well as 28,000 acres of extremely fertile and profitable land. By 1950's Southern standards, he's essentially a king.
Foil: With Maggie. Both of them are charming, manipulative, self-made people who grew up poor and work hard to get what they want. It's why they earn each other's respect.
I Want Grandkids: Never explicitly stated, and he technically already has several from Gooper and Mae, but he clearly wants at least one from his favorite son and beloved daughter-in-law before he goes.
Large and in Charge: It's not just because of his wealth or power that he's called Big Daddy. He's always played by an actor both physically large and with a massive, domineering personality to match; famous examples include Burl Ives, John Goodman, and, in an all-black production, James Earl Jones.
Nouveau Riche: He made his money by working his tail off for years, as opposed to being a Southern aristocrat from the "old" classes.
The Patriarch: Despite only having two children, he's clearly the head of the Pollitt clan, and never lets anyone forget it.
Butt-Monkey: Her maladroit antics are entertaining, but rather painfully, as Big Daddy highlights them to verbally abuse her.
Extreme Doormat: She'll bend over backwards to prevent conflict, to the point of sacrificing her own happiness to make others feel better.
Fat and Proud: She knows she's large and isn't afraid to mention it for the sake of a joke.
Love Martyr: For Big Daddy. As she puts it, she's always loved everything about him: "I even loved your hate. And your hardness."
OOC Is Serious Business: Twice. First, when bumbling, friendly, maternal Big Mama bursts into tears after the latest in decades of rejection by her husband, and second, when she finally Grew a Spine to tell off the meddling Gooper-Mae duo.
Sad Clown: Her antics and attempts at jokes come across as this, as she's clearly devastated by what's happening around her and using humor as a coping mechanism.
Selective Obliviousness: She pretends Brick is still is former youthful golden boy self, acts like her relationship with Big Daddy is healthy, and refuses to acknowledge the idea that he's fatally ill. She's not just an idiot, though; she picks up on the cracks in Brick and Maggie's marriage and shuts down Mae and Gooper's plot to take over the family empire. Heartbreakingly, she even shows a comprehension that Big Daddy doesn't really love her at one point.
Stepford Smiler: Big Mama swears up and down that everything's fine, and that she's happy...even though Big Daddy outright admits he's disgusted by and hates her.
Jerk with a Heart of Gold: Unlike Mae, who comes across as more of a social climber and schemer, Gooper clearly just wants Big Daddy's respect. He remarks that he's spent his entire life doing everything his father asked of him (becoming a lawyer, marrying well, having many children) to please him, and it still hasn't been enough. It's more apparent in the film version, when even he seems to be rooting for Maggie and Brick to reconcile and believes the former when she claims she's pregnant.