What are some quotations that indicate that Hamlet thinks a lot?
In Shakespeare's Hamlet, you can look at virtually any of Hamlet's soliloquies for proof that Hamlet is a thinker.
Let's take his reaction to the 1 Player, for instance, beginning in Act 2.2.515. Hamlet applies the Player's speech to his own situation. There is no inherent connection between the speech and Hamlet's situation, but Hamlet perceives one. He says:
O, what a rogue and peasant slave am I!
Is it not monstrous that this player here,
But in a fiction, in a dream of passion,
Could force his soul so to his own conceit
That from her working all his visage wanned;
Tears in his eyes, distraction in his aspect,
A broken voice, and his whole function suiting
With forms to his conceit? And all for nothing,
What's Hecuba to him or he to her,
That he should weep for her? What would he do
Had he the motive and the cue for passion
That I have? He would drown the stage with tears,
And cleave the general ear with horrid speech,
Make mad the guilty, and appal the free,
Confound the ignorant, and amaze indeed
The very faculties of eyes and ears.
Ideas are proof of thinking, and here the idea is that the actor puts Hamlet to shame. Though he is just acting, he makes his face go pale, forms tears in his eyes, cracks his voice, and makes his whole body reflect the content of his words. Hamlet asks what would the actor do if he had an actual motive for being upset like Hamlet does.
Hamlet proceeds in the speech by rhetorically asking if he is a coward, calling himself a daydreamer, pigeon-livered, and an ass. He puts himself down for a few more lines, but then:
About, my brains. Hum--I have heard
That guilty creatures sitting at a play,
Have by the very cunning of the scene
Been struck so to the soul that presently
They have proclaimed their malefactions;
For murder, though it have no tongue, will speak
With most miraculous organ. I'll have these players
Play something like the murder of my father
Before mine uncle. I'll observe his looks.... (545-562)
Hamlet's brain is so full of thoughts that he interrupts his own self-condemnation and completely changes direction. "About, my brains"--about face, or I must think? His thoughts take an about face. One instant he is nastily condemning himself, and the next instant he is hatching a new plan, a plan to have the actors present a murder scene similar to the murder scene of his father, as told to Hamlet by the Ghost. Hamlet says he will watch the king's reaction, and will be able to tell whether or not the king's reaction is filled with guilt or not.
Thus, Hamlet applies the speech of the actor to his own situation (an idea), then he hatches a plan using the players to prove or disprove the king's guilt (another idea). And he shifts from one train of thought to another in an instant.
Finally, he explains his thoughts by adding that the Ghost could, indeed, be the ghost of his father, but the Ghost could also be a demon come to abuse him, and thereby damn him. Hamlet is a thinker, and he's no fool. He's smart enough to know that the identity of the Ghost is questionable, and that the Ghost could be leading him astray.
Macbeth could have used a bit of Hamlet's brain power: if he'd have tested the witches like Hamlet tests the Ghost, he'd have saved himself and Scotland an awfully lot of trouble. Macbeth needed to stop and think--he needed a "Hum--" instant of thinking.