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:

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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,

For Hecuba!

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:

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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.