Adorkable: Alice. Mostly because of her strange tendencies. She's a bit of a space case, but in an endearing way. Her innocence is also a factor here.
Alternative Character Interpretation: Is Alice: a girl who goes on an adventure, a girl with an impressive imagination, a girl who is going insane, a girl who is high as a kite, or a girl who wants to escape a tragic situation? Your answer will determine which social circle you're allowed to join.
Given the above, Wonderland is also subject to an Alternate Setting Interpretation: Is it merely a dream? The imagination of a bored child? Another Dimension that can be only accessed by a Dream Walker? A dissociative internal headspace for a lonely girl to escape a bad home life? Some combination of two or more of the above? It varies depending on who you talk to.
Most modern adaptations have to explain that "treacle" is a word for molasses,note This is also a case of Separated by a Common Language - it's still called treacle in the UK and that a "cravat" is actually a forerunner to a man's tie. (One adaptation actually has Alice call it a tie.) Some of the humor might go over the heads of modern readers, like the Hatter claiming Alice's hair "wants cutting" (a comment that would have been incredibly rude in Victorian times).
"Mock turtle soup" is a real dish, traditionally made with calf's head meat, which is why the Mock Turtle in Wonderland is traditionally drawn with a calf's head.
Even some British readers may be confused by some references, like the Hatter saying it's always tea time because it's always six o'clock. (Five o'clock tea would not become a tradition in Britain until later.)
Angst? What Angst?: Well, after she almost literally drowned in her own tears, she knew better than to let that emotion get the better of her again.
Awesome Art: As stated, Tenniel's art was the big draw, and has become just as iconic as the story.
"Jabberwocky" somehow manages to be one in spite of the context. Unlike most examples of this trope, however, it is mentioned later on when Alice asks Humpty-Dumpty to translate the poem for her.
"The Lobster Quadrille" and "Turtle Soup", as performed by the Mock Turtle and the Gryphon, are musical interludes that add nothing to the plot.
The scene where Alice sees a giant dog (compared to her), fears it will kill her, but manages to distract it and escape. The dog is the only animal in Wonderland that doesn't talk or exhibit other human characteristics, the tone of the scene clashes with the surrounding scenes, and it is never mentioned again. This isn't ridiculous or over-the-top like a typical BLAM example, but it reads almost like a page from a different fantasy book. Not surprisingly, the Disney movie and most (there is the Hallmark movie) other adaptations leave it out completely. The dog Alice meets in the Tim Burton version may be intended to be a grown-up version of that dog, but it's never clarified one way or the other.
Common Knowledge: The Queen of Hearts and the Red Queen are two separate characters. The Queen of Hearts is a playing card and an antagonist and the Red Queen is a chess piece and, although rather stern, is a good guy who acts as a mentor to Alice. People usually get confused due to several adaptations turning them into one Composite Character. Technically the same applies to Looking Glass Lands and Wonderland proper, yet both places might exist in the same... place.
Diagnosed by the Audience: Fans sometimes guess that Alice is on the autism spectrum, due to her wild imagination, precocious intellect, tendency to talk to herself and play by herself, occasional social faux pas (e.g. praising her cat's skill at catching mice and birds to a crowd of mice and birds), and struggle to understand the world(s) around her. Some also speculate that she has ADHD, due to her impulsiveness and how easily distracted or bored she is at times.
The Mad Hatter, probably the most well known of the characters, other than the Cheshire Cat and Alice herself.
The Gryphon and the Mock Turtle also qualify; diehard fans of the book are prone to expressing disappointment when these two are excluded from adaptations.
Tweedledee and Tweedledum. If an adaptation includes anything from Through the Looking Glass, odds are that it will be them. Their roles in Alice in Wonderland (the Disney movie) probably helped this.
The Jabberwock. It only appears in a minor in-universe poem in Through the Looking Glass, and Alice never encounters it. However, in adaptations it often gains a major role as a dangerous monster that Alice must slay, often as a servant of the Queen of Hearts.
Epileptic Trees: One infamous example from the book involving the term “Painting the Roses red.” Many have interpreted this as a metaphor for menstruation, however this part of the book actually refers to something entirely different. It also doubles as a bit of Genius Bonus.
Fan Nickname: Some fans and adaptations assume Alice's surname is Liddell after the real-life girl that inspired Alice.
Faux Symbolism: The meanings behind "The Walrus and the Carpenter" can be open to interpretation. See the entry in Wikipedia.
Genius Bonus: Math puns. Some more subtle than others. Whenever characters mention numbers or time, it's guaranteed that there's some deeper meaning behind them. Martin Gardner's edition The Annotated Alice attempts to explain all the inside references to math, literature, philosophy, and so on; on many of its pages the Footnote Fever runs longer than the text from the book itself. Then several years later he published a second annotated book completely full of entirely new footnotes.
Germans Love David Hasselhoff: Japan really seems to love Alice in Wonderland, as it's the subject of various forms of Japanese media. The sheer amount of anime, manga, light novels and video games that take inspiration from it are especially noticeable. It's touted as one of the premier examples of fairy tale literature despite not technically being one, as almost anything fairy tale related there will use "Alice" in the name to evoke whimsy as much as English-speaking countries use "Grimm". Alice's Moeness almost certainly helps.
Hard-to-Adapt Work: Alice's Adventures In Wonderland and its sequel are considered "unfilmable," which is pretty remarkable considering that they're also Adaptation Overdosed. The reasons given for this is that the books' verbal charms can't quite translate to a visual medium, and their episodic structure can't quite be reconciled with the three-act structure.
It Was His Sled: The fact that the story turns out to be All Just a Dream is very well known. Though to be fair, it's not like people wouldn't be able to figure this out after reading all this weirdness.
Memetic Psychopath: The Queen of Hearts is often portrayed as a tyrannical villain ruling Wonderland in adaptations, often executing the King of Hearts. However, in the original story, while she does order many executions, none of them succeed and her role is treated as just another strange inhabitant of Wonderland.
One-Scene Wonder: The fawn, it's about the only sane thing in the entirety of the two books.
More people are likely familiar with Tweedledee and Tweedledum from Through the Looking-Glass than the actual poem they're based on.
Several poems in the books, like "How Doth the Little Crocodile", or "You Are Old, Father William", are parodies of Victorian moralistic verses, which were well-known then, but only remembered today because of Alice.
More people know about "I Am the Walrus" by The Beatles than the Through the Looking Glass poem that inspired the song.
Signature Scene: Any proper reference to Alice has at least one Mad Tea Party scene in it (regardless of if the party's actually "mad" or not). Oftentimes the Tea Party will make up the majority of the references to the book. Amusingly enough, in the original version of the story, Alice's Adventures Underground, this scene wasn't present at all, skipping right from the scene where Alice first eats the mushroom to the Queen's croquet grounds.
Tear Jerker: The melancholy poems at the beginning and end of Through the Looking-Glass, "Child of the pure unclouded brow" and "A boat beneath a sunny sky." It's clear how much Carroll missed the happy days he used to spend with Alice Liddell and her sisters.
Values Resonance: The protagonist is a strong female character, and also one allowed to make mistakes and call herself out on her own faults. Also, there is subtle (or not so subtle) lampooning of the stodgy, authoritarian manners of teachers and governesses of Victorian Britain, as well as of the obligatory moralizing of contemporary children's literature, suggesting that a warmer and more empathetic approach to childhood is being promoted.
Viewer Name Confusion: Contrary to popular belief, Carroll never actually refers to any character as "the Mad Hatter" in the book; he is simply called "the Hatter". Alice's name, which was generally left as Only One Name in the books, was never the exact same as her real life namesake, either — Carroll got this Alice's surname from the real one's middle name, and only ever mentioned it once elsewhere.
The Woobie: Poor Mock Turtle! He's a creature that used to be a turtle, but somehow became "mock", whatever that means, and is awfully sad about it. He spends all of his time sobbing, but it's unclear why.
The Ballet
Critic-Proof: All three of the Royal Ballet productions so far have sold out their entire runs (the company even had to add an extra performance when they toured the ballet to Japan), and the National Ballet of Canada did similarly well when they mounted it in 2011 and 2012. Critical reviews, though, were very mixed, with many complaining about the choreography and awkward narrative structure. The revised three-act version has been better received, although there are still a lot of nay-sayers.
Nightmare Fuel: "Pig And Pepper". Dear god, "Pig And Pepper". Especially in the original version. It starts when the Cook opens a window and smoke pours out as she sharpens two oversized meat cleavers. Alice goes inside the house...where everything is bathed in red light and giant pigs are strung up from the ceiling, plus one that's half in a mincer with sausages coming out the other end. The Cook and the Duchess both have blood-stained aprons on, and more than once end up attempting to kill each other. Then, after all that, Alice escapes from the house with the baby (who has by now turned into a pig), only to have it snatched from her by the Duchess who carries it back inside the house while the Cook slams the door brandishing her meat cleaver. Considering that the rest of the ballet is arguably Lighter and Softer than its literature counterpart, this entire section is particularly jarring.
Visual Effects of Awesome: The Cheshire Cat, which is an enormous, illuminated puppet made up of multiple separate parts (four legs, a head, a tail, a torso and hindquarters) and controlled by multiple different people.
Other adaptations
Adaptation Displacement: Movies based on both books are often titled Alice in Wonderland and have left most people unaware that there are in fact two books and many of the cherished elements attributed to the first are actually in the second.
Lampshaded in Sesame Street's Abby in Wonderland. Bert and Ernie appear as Tweedledee and Tweedledum only for a moment when Abby runs past them.
Bert (as Tweedledee): Is that our whole scene? Ernie (as Tweedledum): Well, we're not really in this story. That's a common misconception.
Alternate Character Interpretation: Is Alice simply an imaginative child, or is she actually mad? The level of insanity varies from adaptation to adaptation, with American McGee's Alice being one of the notable examples of the latter.
Big-Lipped Alligator Moment: The 1985 adaptation that has Sammy Davis Jr. as the caterpillar suddenly transform into a human and do a singing and dancing number with Alice, who is suddenly dressed as a boy. After singing an upbeat version of "You Are Old Father William", he goes back to being a caterpillar and both resume their conversation as if nothing just happened.
There was also Carol Channing as the White Queen, turning into a sheep. In the original book she does turn into a sheep as well, but it leads into another scene where Alice is transported into a shop run by the sheep. In the 1985 movie, Alice just runs, and it's never brought up again when she meets the White Queen later. But with Carol Channing's line delivery during the scene, who wouldn't run away?
White Queen: Beeeeeetttteeerrr....muuuuuchhh beeeetttttterrrr....beeeeeeaaaaah *morphs into a sheep*
Genius Bonus: In the 1987 animated television film based on "Through the Looking Glass", a hairy creature called the Snark appears as a tag-along to the Jabberwock and the Bandersnatch. While he may at first glance be an original character created for the film, he's actually a reference to the poem The Hunting of the Snark, which, like Alice's Adventures in Wonderland and Through the Looking Glass, was also written by Lewis Carroll, but isn't as widely known.
On a minor scale, this has also happened to "Twinkle, Twinkle, Little Bat", which is an Affectionate Parody of "Twinkle, Twinkle, Little Star". In both the 1951 Disney version and the 1999 Hallmark version, a musical style of this trope plays when this song is performed.
They Changed It, Now It Sucks!: Some fans of the books base their enjoyment of the various adaptations and reimaginings on how accurate they are to the source material. A few go as far as to say that versions of Alice they don't like (usually Darker and Edgier interpretations) are "the impostor", or that an adaptation/reimagining sucks because it "isn't what Lewis Carroll would want".
. It also doubles as a bit of Genius Bonus.