Orphaned when their parents die in a fire, the Baudlaires now have to escape the greedy hands of Count Olaf...and on their way, they uncover a massive conspiracy.
Badass Adorable: All three. Especially Sunny, who's badass even though she's a baby.
The middle Baudlaire and only boy, Klaus is extremely bookish and prone to using big words. The vast amount of things he's learned from his reading, as well as his research skills, come in handy.
Character Tics: Klaus has a habit of polishing his glasses.
Running Gag: Adults explaining the definition of words to Klaus that he already knows.
Sesquipedalian Loquaciousness: Klaus is fond of big words, much to the annoyance of the villains. He also explains the definitions of words to his siblings often.
The youngest Baudelaire is only a baby and only intelligible to her brother and sister (at least at the beginning). However, she is extremely intelligent, and in addition to having four very sharp teeth as a weapon, she also demonstrates admirable cooking skills later on.
Character Tics: Sunny likes to bare or sharpen her teeth, chews on objects when she's agitated or just for fun and bites people gently in greeting and hard if she doesn't like them.
And in later books, instead of gibberish, she often says words (or partial words) that relate to her response, or at least the topic being discussed. For example, when describing a sword fight, she says "Flynn", when somebody mentions a train, she says "Esoobac", when talking about going undercover, she says "Dragnet", and when somebody asks her to do something impossible, she exclaims "Unfeasi!"
Little Miss Badass: She once fought against a sword-wielding hypnotist with her teeth- and won.
Count Olaf
The main villain of the series. His goal is to get the Baudelaire fortune, no matter where they go and how many stupid disguises he has to wear. He's revealed to have a connection to the shadowy organization known as VFD.
Abusive Parent: To the Baudelaires...an abusive foster parent, anyway.
Pet the Dog: He has a moment with Kit just before his death that qualifies.
Pyro Maniac: It's clear that he has at least burned a hospital, a carnival and a hotel to ground and it's suggested that he also burned the Baudelaires' mansion, but Snicket never confirmed the fact.
In the final book, the Baudelaires confront Olaf over their suspicions of him burning down their mansion. His initial response is "Is that what you think?" followed by "You know nothing."
Villain Decay: Olaf gets less and less threatening as the series goes on. A lampshade is even hung on it when the Baudelaires act annoyed rather than scared in his presence, and near the end, he even gets a Pet the Dog moment.
Woobie, Destroyer of Worlds: Maybe. It's implied that Beatrice and/or Bertrand Baudelaire and/or Lemony Snicket killed his parents with poison darts during a performance of La Forza del Destino.
Esmé Gigi Genevieve Squalor
One of the Baudelaires' many foster parents turns out to be evil and becomes Count Olaf's girlfriend. She's a wealthy woman ridiculously dedicated to keeping up with every ludicrously inane fad that comes about.
The mysterious narrator of the series who holds a torch for a deceased woman named Beatrice.
Alter Ego Acting: Daniel Handler and Lemony Snicket - separate characters in the books themselves.
Author Appeal: Mild example - Daniel Handler is something of a gourmand, and hence the Lemony Narrator never misses an opportunity to describe some delicious dish, even providing a salad recipe in the midst of an urgent-seeming message to his sister embedded in the tenth book.
Plot-Based Photograph Obfuscation: Snicket never shows his face in photographs, but there are several possible explanations for why this is, and most such photographs are only seen by the audience in his author bio rather than by the characters.
This also applies in-universe. A note in the Quagmire diaries indicate that Snicket's face is never seen in a photograph. And indeed, when the Baudelaires find a photo of their parents, there is an unidentified man with his back turned next to them.
Stalker with a Crush: Inverted - Lemony's a good guy, but he does stalk the children of the woman he loved but couldn't have but should have had.
The Woobie: Not even counting the things about his past that are revealed outside of the thirteen books, Lemony has been dumped by his fiancee because she read an unreliable newspaper that claimed he was dead, and then a villain, so he went on the run and STILL is. His beloved married someone else and then died in a horrible fire. Lemony's brother Jacques and sister Kit have both died, and he continues to become entangled in terrible situations as he relentlessly tries to gather information about the children of the woman he loves so that the world will know about the treachery that follows them. This guy's life sucks.
VFD
The mysterious initials of a shadowy organization that everyone - from Olaf to the Baudelaires' parents - is connected to.
The Omniscient Council of Vagueness: V.F.D., and specifically the transcript of the meeting of the vague "Building Committee" in the Unauthorized Autobiography - even the author didn't know some of what was being discussed here, and he was technically in attendance.
The Baudelaires' friends are a identical brother and sister whose brother Quigley died in a fire. Referring to themselves as "triplets" (just because Quigley's dead doesn't mean they were born twins), they help the Baudelaires out and get kidnapped for their trouble. Duncan is a journalist while Isadora is a poet specializing in couplets. Later on, Quigley is revealed to have survived.
Enfante Terrible: She is rude, violent, filthy, but apparently one of the most popular girls in her school, and in her later appearance is to be crowned "False Spring Queen."
Tyke Bomb: In her second appearance, Count Olaf and Esmé Squalor adopt Carmelita Spats as a Tyke Bomb, but she's so thoroughly spoilt by Esmé as to be utterly unhelpful, and after demanding lessons on how to spit in exchange for shooting someone with a harpoon she's ditched by Olaf; he later turns his attention to Sunny as a possible replacement.
Count Olaf's Troupe
Olaf has a large variety of henchmen he calls his "acting troupe."
Ambiguous Gender: The Person of Indeterminate Gender, a.k.a. the enormous person who looked like neither a man or a woman.
Ensemble Darkhorse: Several members of Olaf's troupe, perhaps because of the Yaoi Fangirls; Fernald, in particular, was much more popular after Book the Eleventh, but then he was never seen again.
Screw This, I'm Outta Here: The white-faced women fall victim to this in Book the Tenth, as apparently do Fernald and Fiona in Book the Twelfth (albeit off-screen).
The Trope without a Title: The white-faced women, the man with a beard but no hair... pretty much most of the troupe.
To elaborate, in one of Snicket's rambling letters in The Beatrice Letters, there is this gem of a line: "I will love you until C realizes that S is not worthy of his love." The whole letter is about VFD members, and he uses their initials as their codenames, and Charles is very much Sir's Dogged Nice Guy.
I Just Want to Be Normal: Hugo, Colette, and Kevin, the "freaks," are a hunchback, contortionist, and ambidextrous, respectively. Subverted by the fact that most people do indeed think they're disgusting freaks.
Suspiciously Similar Substitute: Charles, Jerome and Hector are all good-hearted and well-meaning men whose cowardice causes them to fail the Baudelaires.