Question

What is hamlet debating in his famous "to be or not to be" soliloque

Answer 1

Hamlet is debating whether or not to kill himself, whether it is nobler to stay, endure the misery, and fulfill his promise to his father to kill Claudius, or to kill himself and end his suffering now.
"To be or not to be, that is the question" (Act 3, Scene 1, Line 64-98).