"Well, I'd better have a look."
The Cheshire Cat says this to Alice once he learns the Bandersnatch has scratched her arm. Just before this Alice believed she was merely in a dream and nothing could harm her, but the Cheshire Cat points out that the Bandersnatch really hurt her in the chase.
"The Jabberwock, with eyes aflame, jaws that bait and claws that catch, beware the Jabberwock, my son, The frumious Bandersnatch. He took his vorpal sword in hand, the vorpal blade went snicker-snack. He left it dead, and with its head, he went galumphing back. Its all about you, you know."
The Mad Hatter is telling Alice of her destiny to destroy the Jabberwocky by quoting the original poem "The Jabberwocky" by Lewis Carroll. Screenwriter Linda Woolverton takes some liberties with the original poem in order to fit it into the plot of the film. In this context, it serves as yet more evidence that the Mad Hatter really is mad, given that the words don't seem to make much sense.
"I'm sorry, Hamish. I can't marry you. You're not the right man for me. And there's that trouble with your digestion."
At the end of the film, Alice returns to the garden party and upon doing so tells Hamish immediately that she cannot marry him. She has just experienced her destiny at work in Wonderland and now that she is back in her real life, she is much more self-confident and decisive. She does not stammer or stall to articulate her intentions and needs, and tells Hamish outright that they are not a match, even making a crack about his sensitive stomach.
"You used to be much more..."muchier." You've lost your muchness."
When the Mad Hatter first encounters Alice at his tea party, he is disappointed to find that she does not have the same spark—which he calls "muchness"—that she did as a child. He finds that some of her imagination and sense of possibility has been dulled by age, and he comments on it.
Alice: This is impossible. The Mad Hatter: Only if you believe it is.
Before she goes to fight the Jabberwocky, Alice worries that slaying it will be impossible. She is discouraged and unsure about her own powers, but the Mad Hatter assures her that the task is only impossible if she doesn't believe in herself. It is this little encouragement that motivates Alice to walk towards the battlefield to try her fate.
"It is far better to be feared than loved."
At one point, the Knave tells the Red Queen that it is better to be feared than loved. She is not completely sold on the idea at first, as she has always wanted to be loved, but was outshined by her sister. Later in the film, when she begins to lose favor with her courtiers, and realizes that her power is dwindling, she doubles down in her tyrannical attitudes and echoes the line, affirming the Knave in his conviction that it's better to be feared than to be loved.
"Why is a raven like a writing desk?"
The Mad Hatter says this over and over throughout the film. It is almost like his catchphrase, but he never answers his own riddle. It is yet more evidence that he has lost his mind.
"Off with their heads!"
This is what the Red Queen says whenever someone displeases her and she wants to have them executed. She screams it in a shrill voice, an order that no one can ever challenge. In fact, it is one of the most iconic lines from Lewis Carroll's original novel, uttered by the Queen of Hearts, on whom the Red Queen is partially based.
"I'm afraid so. You're entirely bonkers. But I'll tell you a secret. All the best people are."
In the beginning of the film, Alice asks her father if she is insane and he tells her that she is, but then adds this line, assuring her that "all the best people are." He takes something that seems like a negative designation and turns it into a positive attribute. With this line, the viewer sees that Alice's father encourages her to be imaginative, to think outside the box, and celebrate and cultivate her own special "madness."
"Who are you?"
This is another line from the original novel by Lewis Carroll, and Absolem says it several times throughout the film. In one way, he is asking Alice to introduce herself straightforwardly, but on another level, he is asking Alice to believe in who she is, and assert herself with confidence. It is as much a question about identity as it is a simple question.
