Adorkable: 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. Many adaptations (the Disney version and the 1999 Hallmark version, for example) end up taking Alice's adorkableness Up to Eleven
Genre Savvy: After finding the "DRINK ME" bottle, Alice decides not to just immediately drink from it and instead checks to see if it's also labeled "poison".
...for she had read several nice little stories about children who had got burnt, and eaten up by wild beasts, and other unpleasant things, all because they would not remember the simple rules their friends had taught them.
Hair of Gold: Usually depicted with this, the most notable exception being the 1999 version.
Kindhearted Cat Lover: She adores her cat Dinah (and in the book extends the same adoration to Dinah's two kittens), and gets along famously with the Cheshire Cat, whom she calls "Cheshire-Puss".
Literal-Minded: A few times; for example, when the Mouse says that he has a "long, sad tale", Alice assumes he means his tail and comments "it is very long, but why do you call it sad?" The proceeding tale is actually shaped like a tail.
Adapted Out: Snowdrop (the white kitten) and Kitty (the black kitten), who are Dinah's kittens, appear only in the book of Looking Glass. They never appear in any adaptations, where Dinah is the only real-world cat to appear (and is often portrayed as a kitten herself).
And You Were There: Played with in Looking Glass. As Alice wakes up, the Red Queen "turns" into a kitten in her hands, and she discovers that she's holding an actual, purring kitten (the kitten she fell asleep cuddling). Alice takes this as a sign that all three cats were with her in her dream. She identifies the black kitten as the Red Queen and the white kitten as the White Queen, and after a bit of thought decides that Dinah must have been Humpty Dumpty.
Cute Kitten: Dinah in the Disney version (and in several other adaptations). Snowdrop and Kitty in Looking Glass.
A Kitten Named Kitty: While Dinah and Snowdrop have proper names, the black kitten is never called by any name other than Kitty and is usually referred to as "the kitten" by the narrative.
The Unseen: Dinah in the first book. Though Alice often talks about her (especially in earlier chapters), she never actually appears. She does appear in the second book, with her two kittens.
Self-Deprecation: A rumored reason as to why Dodgson specifically chose a dodo as his caricature was a speech impediment he had that caused him to stutter. As such, he would introduce himself as "Do-Do-Dodgson".
Serious Business: He and the other birds and animals take the prizes at the end of the Caucus Race very seriously. Alice finds this very silly, but decides it would be rude to laugh after seeing just how serious they are about it.
The Omniscient: A common portrayal of him in adaptations and reimaginings is that he knows absolutely everything (American McGee's Alice and the Tim Burton adaptation are standouts here). In the book, we have no confirmation that he's omniscient, but compared to all the other animals in Wonderland, he might as well be.
Only Sane Man: Probably the most level headed individual in Wonderland.
Power Glows: In the 1999 Hallmark adaptation, especially when he turns into a butterfly.
The Caterpillar, now a Butterfly:THE MUSHROOM, OF COURSE!
Telepathy: Implied; he's prone to responding to things that Alice thinks as though she said it out loud.
Ambiguous Gender: A lot of the animals in Wonderland lack established genders (even the Dodo and the Cheshire Cat were referred to as "it"s by the narrative) but this one is especially confusing; the Pigeon apparently has eggs to hatch, which is why it's so afraid of serpents, but it's never established if it laid the eggs (which, for obvious reasons, would designate it female) or was just hatching them (a job that would go to either gender).
No Sense of Personal Space: When in a good mood, something that Alice finds rather disquieting. She's exactly the right height to rest her chin on Alice's shoulder, unfortunately for Alice.
The Cheshire Cat
Adaptational Villainy: In the book, he's the closest thing Wonderland has to a Nice Guy and is the only character Alice thinks of as a friend. Quite a few adaptations, including the Disney movie, turn him into a callous Jerkass, and some of them even make him directly sinister and dangerous.
Affectionate Nickname: Alice calls him "Cheshire-Puss". His reaction implies that he likes this nickname a lot.
Cats Are Magic: He has abilities that no other Wonderlanders seem to possess, being able to disappear and re-appear at will.
Dark Is Not Evil: He's somewhat creepy looking (Alice decides to approach him cautiously, after observing his large amount of teeth and sharp claws) but is pretty much the friendliest individual Alice meets in Wonderland.
Genre Savvy: He tells Alice that she can't help going among mad people in Wonderland and that it's best just to go along with it. Later, he materializes in the Queen's croquet ground as nothing but a head, presumably to avoid being beheaded by the Queen (or to mess with her).
Jerkass: The Disney version, possibly as an instance of Cats Are Mean. Though not overly malicious and seeming friendly in his first two appearances, in the later parts of the film he seems to go out of his way to get Alice into trouble, for no good reason.
This counts mainly for the actual movie, though. In later appearances in other stories and spin-offs, he's been softened up a bit and is more of a Blue and Orange Morality type.
His portrayal in the Kingdom Hearts series is mainly neutral. He does help Sora with proving Alice's innocence, but later on sends a Trickster to attack him. He's at his worst in the manga adaptation for Kingdom Hearts: 358/2 Days, where he throws a hedgehog at the Queen of Hearts and frames Roxas for it.
Kick the Dog: The Disney version. After letting Alice take the blame for his pranks against the Queen, he vanishes, only to return at the end of Alice's trial, after Alice's failed attempt to stand up for herself, to make sure things go as bad as possible for her:
Alice: Now as for you, Your Majesty... *starts shrinking* "Your Majesty," indeed! Why, you're not a queen! You're just a fat, pompous, bad-tempered old — *finally realizes she has shrunk down to normal size and is smaller than the Queen* — tyrant. Queen of Hearts:*smiling dangerously* And what were you saying, my dear? Cheshire Cat:*suddenly appears* Well, she simply said you're a fat, pompous, bad-tempered old tyrant! *laughs and disappears again* Queen of Hearts:OFF WITH HER HEAD!
Seems like some people at Disney thought this made him too much of a Jerkass, though, and in one of the Recursive Adaptation novelizations of the movie, this part is actually changed to the Cat redeeming himself with a pseudo-Big Damn Heroes moment; instead of showing up to make things worse for Alice at the trial, he shows up to confess, and to distract the Queen and the guards with a lot of nonsense, some of which is taken directly from the original book, allowing Alice to escape in the confusion.
Cheshire Cat: (while standing on his own head) Can you stand on your head?
Cheshire Cat: (while slowly disappearing) You may have noticed that I'm not all there myself.
Nice Guy: By Wonderland standards, anyway. In the book, he's without question the friendliest character Alice meets, being the only one who actually listens to her without getting unreasonably offended or start insulting or threatening her. It's telling that when he reappears, Alice is actually glad to see him.
This carries over into the 2010 adaptation as well; the first thing he does on screen is ask Alice where she got her wounds, then offer to use his reality warping to heal them for her. When she refuses, he politely asks if he can at least bandage it for her.
Only Sane Man: In the Duchess's house, at least. Subverted, though, in that he proudly considers himself mad.
Reality Warper: Is capable of things that other Wonderlanders aren't, such as turning invisible, teleporting and even taking himself apart. While in the book he only seems to be able to affect himself, adaptations tend to ramp his reality bending powers Up to Eleven until he's basically the Wonderland equivalent to Q. In the 2010 film, he even transforms into the Hatter to save him from execution.
Aww, Look! They Really Do Love Each Other: At the beginning, Alice complains about her sister's activities not being exciting enough, but at the end she's all too happy to share the details of Wonderland with her.
No Name Given: Though she was based off of Alice's real life sister, Lorina so some adaptations give her that name.
Only Sane Woman: Although she never goes to Wonderland, she could be seen as this with Alice, at least. She is the Only Sane Character overall, though.
The Dreaded: Implied, since in the poem, his death is met with much rejoicing. It's also implied that the only reason he hasn't already been slain is because everyone in the village was just too terrified of him to go after him.
The theory about the White Knight is widely believed by most scholars, however (given the fact that he was the only character in either book who seemed genuinely kind and polite to Alice, seemingly representing Dodgson's friendship with the girl he based the character on), although Dodgson himself never confirmed nor denied it.
Bungling Inventor: Figures out a fantastic way to keep his sandwiches dry in case of wet weather: he simply fastens his lunchbox to his saddle upside down! However, he, ah, forgot to fasten the box shut properly...
Ditzy Genius: Is a smart inventor, but is forgetful with most things.