O, that this too, too solid flesh would melt,
Thaw and resolve itself into a dew!
(Hamlet, Act 1 Scene 2)

Neither a borrower nor a lender be, 
For loan oft loses both itself and friend, 
And borrowing dulls the edge of husbandry.
(Polonius, Act 1 Scene 3)

...though I am native here
And to the manner born, it is a custom 
More honoured in the breach than the observance.
(Hamlet, Act 1 Scene 4)

Something is rotten in the state of Denmark.
(Marcellus, Act 1 Scene 4)

That one may smile and smile and be a villain.
(Hamlet, Act 1 Scene 5)

There are more things in heaven and earth, Horatio,
Than are dreamt of in our philosophy.
(Hamlet, Act 1 Scene 5)

Brevity is the soul of wit.
(Polonius, Act 2 Scene 2) 

Though this be madness, yet there is method in't.
(Polonius, Act 2 Scene 2) 
(This is often summarised or misquoted as: 'There's method in his madness')

There is nothing either good or bad but thinking makes it so.
(Hamlet, Act 2 Scene 2)

O, what a rogue and peasant slave am I! 
(Hamlet, Act 2 Scene 2)

To be, or not to be, that is the question.
(Hamlet, Act 3 Scene 1)

The lady protests too much, methinks.
(Gertrude, Act 3 Scene 2)
(This is often misquoted as: 'Methinks the lady doth protest too much')

How all occasions do inform against me, and spur my dull revenge. 
(This famous soliloquy by Hamlet appears only in the Second Quarto in an extended Act 4 Scene 3)

Alas, poor Yorick! I knew him, Horatio: A fellow of infinite jest.  
(Hamlet, Act 5 Scene 1)
(This is often misquoted as: 'Alas, poor Yorick, I knew him well')

If it be now, 'tis not to come: if it be not to come, it will be now: if it be not now, yet it will come: the readiness is all.  
(Hamlet, Act 5 Scene 2)

The rest is silence. 
(Hamlet, Act 5 Scene 2)

Goodnight, sweet prince,
And flights of angels sing thee to thy rest!
(Horatio, Act 5 Scene 2)