"The Lobster Quadrille" and "Turtle Soup", as performed by the Mock Turtle and the Gryphon, are musical interludes that add nothing to the plot.
Come for the X, Stay for the Y: When Alice's Adventures in Wonderland was released, it was the illustrator, John Tenniel, who was the big draw to the book — he was very popular and well-regarded, and who had heard of "Lewis Carroll" anyway? But it turned out, children were delighted by Alice's nonsense world, and especially the gift of a story without a moral in it!
Common Knowledge: The Queen of Hearts and the Red Queen are two separate characters. People usually get confused due to Composite Character. Technically the same applies to Looking Glass Lands and Wonderland proper, yet both places might exist in the same... place.
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.
"Weird Al" Effect: 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.
A number of fans and/or Moral Guardians seem to believe that Carrol was totally high when he wrote the stories, rather than simply an eccentric man who liked wordplay, satire and logic games. The Annotated Alice argues that specific surreal elements of Wonderland are clues that it's all a dream.
That said, he almost certainly would have exposed himself to something with hallucinogenic properties while writing the books. Patent medicines were ubiquitous in his time, and they're infamous for having contained substances like cocaine and heroin that far back - even cough medicine would likely have contained something fishy by today's standards. The better question wouldn't be whether or not it was made on drugs, it would be how much of a creative influence the drugs actually were at all.
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.
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.
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.
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/Fridge Brilliance: 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 Carrol, 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 1950 Disney version and the 1999 Hallmark version, 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".