Who needed a brain in Alice in Wonderland?

Answer 1

In Alice in Wonderland everybody (who needed one) had a brain.

In the poem You Are Old Father William, Father William claims not to have a brain, but gives no indication that he actually wants one:

"You are old, father William," the young man said,

"And your hair has become very white;

And yet you incessantly stand on your head--

Do you think, at your age, it is right?"

"In my youth," father William replied to his son,

"I feared it might injure the brain;

But now that I'm perfectly sure I have none,

Why, I do it again and again."

In The Wizard of Oz, however, the Scarecrow wanted a brain very much.