Angst? What Angst?: Averted for the most part. Most of the unfortunate events that happen to the Baudelaire orphans affect them significantly, and they frequently discuss (even under rare good circumstances, as in the early chapters of The Reptile Room) their sorrow over events that have happened a significant amount of time in the past. Their conflicts are treated as sufferings rather than fun adventures, and when characters do respond with unusual positivity to terrible things, it's noted and generally played up for absurdity.
Alas, Poor Villain: Olaf's death and last words carry a perhaps surprisingly emotional tone.
Canon Fodder: While the series was going on, it was assumed that all the loose ends and questions would eventually be resolved or answered, leading to huge amounts of speculation. Most of it was never referred to again.
Cargo Ship: In The End, Olaf embraces his weapons — a harpoon gun and a container of poisonous mushrooms — as if they're the only things he loves.
The Chris Carter Effect: Invoked Trope by the author (one of the major messages of the series being that "not all mysteries can ever be solved, better to accept this and move on"). There is a seriousBroken Base on whether or not deliberately invoking the Trope at all (let alone for the sake of An Aesop) and then going ahead with putting a massive amount of unsolved mysteries on the story makes it any less of a Troll act on the part of the author.
Comic-Book Time: A possible/subtle example. Duncan and Isadora say they spent three semesters at the academy before the Baudelaires arrive. "The Slippery Slope" later establishes the Quagmire fire as happening after "The Reptile Room". Excluding the last Chapter, Violet and Klaus only have one birthday each throughout the series.
Even before we had much Belated Backstory for them, Fanon interpreted Olaf's assistants as Yaoi Guys, or certainly something far more complex and sympathetic than they appeared in canon.
Thanks to her clingy unlucky husband, Esmé often gets this treatment. And Carmelita too, since she acts as her surrogate mother.
Ear Worm: If you listen to the audiobooks, Tim Curry's rendition of "Volunteers Fighting Disease" song will never leave your head. NEVER.
Epileptic Trees: A rather pervasive bit of Fanon holds that everyone and everything the Baudelaires encounter is part of a plan arranged by an Ancient Conspiracy with the purpose of training them for V.F.D. Theories of the "Minor Character X is really Character Y/one of the Baudelaire parents/Lemony Snicket" sort also show up.
Everyone Is Jesus in Purgatory: One can make a somewhat reasonable case for the series being an allegory for the history of the Jewish people, and Daniel Handler has himself noted that the series contains Jewish themes. Snicket's frequent use of Meaningful Names and literary allusions has also inspired a fair amount of over-interpretation.
Fashion-Victim Villain: Esmé wears many elaborate and unusual outfits over the course of the series. Count Olaf also wears strange outfits as part of his disguises.
Growing the Beard: The whole Mind Screw started and was hinted from the third book onwards, but it's after The Austere Academy when things really took off. That's because when he was writing the fifth book Handler had finally had his contract signed for 13 installments and could plan ahead the plot.
You could say that The Miserable Mill also grew the beard since it revealed there was a connection between Lemony and the life of Count Olaf. Monty's death in The Reptile Room was also a key emotional step.
Harsher in Hindsight: In The Wide Window Lemony says Josephine's fear of realtors is irrational because nothing bad has ever come out of the industry, which is rather awkward after the 2007 housing bubble collapse. This is actually acknowledged in the Netflix series, as he still says the line but then looks embarrassed by it.
Idiot Plot: One of the reasons why the books have plots after the first few is because the Bauderlaires are some of the few recurring characters that do not have the Idiot Ball. Tropes Are Not Bad because it adds to the dark humor, and the feeling of bleakness in a world going out of it's way to be cruel to these children.
Inferred Holocaust: Considering the huge number of buildings that get torched in the series, it's to be expected. However, it's also deconstructed in the sense that when it's the Baudelaires' turn to start burning things, they admit that they have no idea how many people die as a result of their actions, and are deeply affected by it, most notably in the destruction of the Hotel Denoument, where even the author isn't sure of the death toll. The book even ends with one: there's the potential for the islanders to spread their poisoning to the mainland, though it's acknowledged that this is unlikely.
The Baudelaire children. Their parents are killed in a house fire and they're being pursued by a relative who wants their fortune. To add to their woobieness, their relatives are killed off and their only friends get taken away from them.
The Quagmires. Just like their friends, their parents have been killed in a mysterious accident and two of the siblings believe their brother has died. They're also pursued for their fortune and have been held captive for who knows how long. In Duncan and Isadora's final appearance, they're separated from their friends again, but it's never explained what happened to them.
Les Yay: "Although sadly I believe it will be quite some time before two women can be allowed to marry and I will love you if you have a child, and I will love you if you have two children, or three children, or even more, although I personally think three is plenty, and I will love you if you never marry at all, and never have children, and spend your years wishing you had married me after all, and I must say that on late, cold nights I prefer this scenario out of all the scenarios I have mentioned.”
For those who don't know, this is the full quote "I will love you if you marry someone else–your co-star, perhaps, or Y., or even O., or anyone Z. through A., even R.–although sadly I believe it will be quite some time before two women can be allowed to marry." This is from The Beatrice Letters and is from LS to BB (Lemony Snicket to Beatrice Baudelaire). "R" is also believed to the R Duchess of Winnipeg, whose ring Bertrand used to propose to Beatrice.
Memetic Molester: Count Olaf. On top of being creepy as all hell, the part where he "marries" Violet certainly enforces this.
Misaimed Fandom: There are some fans who interpret the series as a serious drama rather than a dark comedy. While the series has plenty of dark and depressing moments, there are also plenty of absurd, comical scenes to balance it out.
Count Olaf's schemes to get the fortune become more terrifying as the books go on.
The descriptions of the Medusoid Mycelium slowly growing in its victims' throat and mouth. Doubles as Nausea Fuel.
No Yay: Count Olaf's affections for Violet are always portrayed as disturbing by the fanbase.
Paranoia Fuel: Beneath the surface of society is a violent feud going back decades between two factions of a child-stealing conspiracy, many members of which lead elaborate double lives as respectable members of the community while in secret they have few compunctions about arson or murder; your parents, teachers and especially librarians are probably in on it, and so are waiters and hotel managers, while taxi drivers are just waiting to whisk you away to a new life.
Periphery Demographic: Like Harry Potter, it's one of those books you'll often see teens and adults picking up for themselves, possibly not allowing their own children to read them until they are mature enough that it won't give them nightmares.
An emotional example: The first time reading the books is easier to laugh at the wacky and absurd situations and the Deus Angst Machina because, in spite of the multiple warnings, it's easy to hope that at the end there will be a somewhat satisfactory conclusion and things will turn out well for the children. The second time around, when you are painfully aware of all the despair and misfortune awaiting the kids at every turn that will in all probability continue long after the end of the books, even the wackiest setback can become a Tear Jerker.
There's a surprisingly uplifting bonus: If you followed the series as each book came out, it was pretty easy to forget some of the many references to the future, long after the series finishes, that the narrator made in the earlier books. While the final book pointedly refuses to give a satisfying conclusion, and indeed an unhappy story is what the narrator had often called this entire saga, there are several small hints that the Baudelaires have quite a future ahead of them after all. In The Wide Window, it's definitively stated that Violet would return to Briny Beach for a third time, and since she hadn't by The End, she must have survived. In The Reptile Room Klaus is said to, after many years, still be wishing he called the taxi driver to take "Stefano" back, implying, though with much less evidence, that he too survived. And, in the Beatrice Letters, Sunny is mentioned as sharing her recipes on the radio when she grows up to be a young woman, which is the strongest evidence of a happy ending for any of these characters. Suddenly, a book series that's famous for its unfortunate events and inconclusive ending ends up with a heartwarming moment via a good rewatch!
Ship Mates: Violet/Duncan or Violet/Quigley end as this with Klaus/Isadora.
Spoiled by the Format: The Baudelaires' fortune will be legally theirs once Violet turns 18. It takes 11 books for her to reach her 15th birthday, and the series ends when she's roughly 16. Though by that point the Baudelaires stop caring about their fortune and are more concerned with surviving.
What an Idiot: On no less than four separate occasions in The Carnivorous Carnival it is shown pretty clearly that Count Olaf knows exactly who the Baudelaires are, and these kids, who have been so good at catching on to these sorts of things previously, miss it every time. To clarify:
1. After revealing their true identities to Olivia, Count Olaf comes bustling out of her tent the next day to exclaim "I've got what I wanted!" before pointing directly at the Baudelaires.
2. On their way to the lion show, Olivia hands Violet the last ingredient needed for their escape vehicle and refuses to answer their questions, pretty clearly implying that she has betrayed them and wants them to escape while they can.
3. Olaf relentlessly trolls them after the lion show, menacingly pointing at Klaus and saying "I think you're lying to me..." after Klaus has insisted that there's nothing else useful in the tent. Of course, two seconds later he's supposedly talking about the food left in the tent.
4. Not much later, Olaf decides to keep Chabo/Sunny with him in his car, even though he has no reason to do so and it's even said that the car is overcrowded. Of course, it would have probably been too late for the Baudelaires even if they had caught wise by this point...
What Do You Mean, It's for Kids?: The title should have been a warning, as should the actual warning, but this series contains plenty of dark material, not to mention a vast array of references and allusions that children would not likely understand.
Woolseyism: Since "VFD" originally stood for Volunteer Fire Department, the initialism can vary wildly in different languages, so other names using the initialism are adjusted accordingly. For instance, in Greek, "VFD" becomes "Ε.Α.Π.", so the "Village of Fowl Devotees" has to become "Επαρχία Αρπακτικών Πτηνών" or "District of Predatory Birds". In some languages, there's even a modified logo; for instance, the French "VDC" logo looks like this.