What characters display guilt in Shakespeare's Hamlet? What are the quotes that indicate it?

Just as dstuva said so well above, the most guilty
individual in the play is King Claudius. Although he never comes right out and says he
is sorry for what he has done, he cannot pray and knows full well that he is a guilty
murderer and despicable liar.

And, yes, Hamlet, too, feels
guilty for not acting with more haste to exact the revenge that his father's ghost so
sorely needs.

But there is one more person who, although
she can perhaps be excused for her weakness, also bears some guilt and feels it. That
person is Hamlet's mother, Queen Gertrude.

After the
play-within-the-play and just after Hamlet spares Claudius' life while he is kneeling in
ineffectual prayer, Hamlet goes to see his mother in her chamber. He is pretty rough
with her and rightly so; she has, out of weakness and ignorance, married her dead
husband's killer. The ghost intrudes on the scene  in order to prod Hamlet to get on
with his revenge, and then Hamlet says to his mother (Act 3, Scene
4):

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HAMLET:

...It is
not madness

That I have utt'red. Bring me to the
test,

And I the matter will reword; which
madness

Would gambol from. Mother, for love of
grace,

Lay not that flattering unction to your
soul

That not your trespass but my madness
speaks.

It will but skin and film the ulcerous
place,

Whiles rank corruption, mining all
within,

Infects unseen. Confess yourself to
heaven;

Repent what's past; avoid what is to
come;

And do not spread the compost on the
weeds

To make them ranker. Forgive me this my
virtue;

For in the fatness of these pursy
times

Virtue itself of vice must pardon
beg

Yea, curb and woo for leave to do him
good.

QUEEN:

O Hamlet, thou
hast cleft my heart in
twain.

And with that last
line, Gertrude, at least in part, admits to some guilt in her actions. She then comes to
believe in her son and his cause and agrees to do her best to, finally, act with honor
and intelligence.