Big Breast Pride: She displays this on numerous occasions. Not that she goes out of her way to emphasize them (except in the first season finale with Martha Stewart...) but when they're noticed, she generally reacts with pride, as well as amusement when others notice the patently obvious.
Deadpan Snarker: One couldn't imagine the show without her snide one-lines.
Double Entendre: Spits out these frequently. Especially involving any version of the word "come".
High School Bully All Grown Up: Mentioned once she was something of a bully in school, when Caroline met one of Max's old teachers, with Caroline acknowledging that she's not quite grown out of it.
Teacher: You look just like the girls Maxine used to give wedgies to.
Caroline: Still does.
Jerk with a Heart of Gold: Despite regularly being snide and sarcastic, she genuinely felt bad for Caroline and allowed Caroline to stay in her home without really asking for anything in return. It's pretty much established at the end of "And The Reality Check" that she's rather nice as Max is holding back tears as Chestnut is sent away for the winter. She's either a golden-hearted jerkass or possibly a Knight in Sour Armor.
The Stoner: Not overemphasized, but Max is indicated to be a pot smoker, with "And the High Holidays" even acknowledging that she has a dealer.
Supreme Chef: Max is this when it comes to cupcakes, although she may also be a One-Note Cook. Ultimately subverted in "And The Secret Ingredient": She uses store-bought cake mix because she never learned how to make cupcakes from scratch.
Tomboyish Name: She goes by "Max" which is more often than not a man's name.
Sugar and Ice Personality: Tends to be snarky regularly insults just about everyone, but tends to be somewhat compassionate at times.
Wake Up Make Up: Hands down the most blatant example of the cast and perhaps also of the current TV landscape, she sports her dark red lipstick and heavy eye makeup even during bedtime and in the bath tub.
Played by: Beth Behrs
A-Cup Angst : Not so much on Caroline's part, but Max frequently teases her about her chest.
Daddy's Girl: She's got a very close relationship to her father due to having a Missing Mom and being treated like a princess for her whole life.
Ditzy Genius: She has some hilariously naive beliefs about poverty and sexuality ("Max, you can't get pregnant doggy-style!"), and yet she's got a degree and when dealing with her and Max's cupcake business, displays lots of business sense.
Dumb Blonde: She surprisingly averts this trope; while she's definitely naive, she's far from stupid and can hold her own in a lot of areas.
Hair of Gold, Heart of Gold: She's grossly naive when it comes to the lower-class lifestyle, but doesn't let it get in the way of her helping Max and others.
Missing Mom: Her mother cheated on her father and was gotten rid of... in a society way, much worse than in the Mob way.
Riches to Rags: Before her dad went to jail for his Ponzi Scheme, her family had a ten-figure net worth.
Played by: Matthew Moy
Ambiguously Gay: In one episode Han is seen entering the men's room or a movie theater with another man. Another episode has him admitting to having paid for sex. He also mentions a homosexual experience in college, but quickly backtracks upon apparently realizing it wasn't one. Max makes make one or two closet jokes about him as well.
Audio Erotica: In one episode, Max and Caroline overhear him speaking on his cell phone in Korean. They both state that he sounds very attractive. And they weren't even being sarcastic!
Butt Monkey /Chew Toy: He is usually the butt of many jokes. Usually involving his height or the fact he could be mistaken for a woman or a young boy. Taken Up to Eleven by Sophie in "And The Pearl Necklace"
Older Than They Look/Younger than They Look: Sounds weird, doesn't it? Due to his shortness and finical behaviour, the diner employees alternate between calling him an old man and a freaky child. He's 29, actually.
Good Adultery, Bad Adultery: His wife and him have an open relationship and she not only seems to tolerate but actively encourage him and Caroline to have an affair. Caroline's stance on this is different.
Innocent Innuendo: Pretty much every character makes a sex joke every other line. Nicolas is the only one who does it without knowing!
Meta Casting: Sort of. Marini is a baker's son and was quite talented as a youth.
Mr. Fanservice: Easily the most conventionally attractive male cast member