Shakespeare was not immune to the theatrical allure of the gallows.  He mentions hanging (literally or by the popular oath "go hang" in all of his plays)  The following is a list of plays with interesting execution references or discussions:

Love's Labour's Lost
Titus Andronicus
King Henry VI, Part 2
Hamlet
Macbeth
Cymbeline
The Tempest

Biron
I could put thee in comfort.  Not by two that I know:
Thou makest the triumviry, the corner-cap of society,
The shape of Love's Tyburn that hangs up simplicity.

Plains near Rome.

[Now a prisoner of the Goths led by Lucius, Aaron is led onstage carrying his child.]

Lucius
O worthy Goth, this is the incarnate devil
That robb'd Andronicus of his good hand;
This is the pearl that pleased your empress' eye,
And here's the base fruit of his burning lust.
Say, wall-eyed slave, whither wouldst thou convey
This growing image of thy fiend-like face?
Why dost not speak?  what, deaf?  not a word?
A halter, soldiers!  hang him on this tree.
And by his side his fruit of bastardy.

Aaron.  Touch not the boy; he is of royal blood.

Lucius
Too like the sire for ever being good.
First hang the child, that he may see it sprawl;
A sight to vex the father's soul withal.
Get me a ladder.

[A ladder is brought, which Aaron is made to ascend.]

Aaron
                    Lucius, save the child,
And bear it from me to the empress.
If thou do this, I'll show thee wondrous things,
That highly may advantage thee to hear:
If thou wilt not, befall what may befall,
I'll speak no more but 'Vengeance rot you all!'

Lucius
Say on:  an if it please me which thou speak'st
Thy child shall live, and I will see it nourish'd.

[Sound trumpets.  Enter King Henry VI, Queen Margaret , Gloucester, York, Suffolk, and Salisbury; the Duchess, Margaret Jourdain, Southwell, Hume, and Bolingbroke, under guard.]

King Henry VI
Stand forth, Dame Eleanor Cobham, Gloucester's wife:
In sight of God and us, your guilt is great:
Receive the sentence of the law for sins
Such as by God's book are adjudged to death.
You four, from hence to prison back again;
From thence unto the place of execution:
The witch in Smithfield shall be burn'd to ashes,
And you three shall be strangled on the gallows.
 
You, madam, for you are more nobly born,
Despoiled of your honor in your life,
Shall, after three days' open penance done,
Live in your country here in banishment,
With Sir John Stanley, in the Isle of Man.

Duchess.  Welcome is banishment; welcome were my death.

Gloucester.  Eleanor, the law, thou see'st, hath judged thee:
 I cannot justify whom the law condemns.

[Exeunt Duchess and other prisoners, guarded.]

First Clown
What is he that builds stronger than either the
mason, the shipwright, or the carpenter?

Second Clown
The gallows-maker; for that frame outlives a
thousand tenants.

First Clown
I like thy wit well, in good faith:  the gallows
does well; but how does it well?  it does well to
those that do in:  now thou dost ill to say the
gallows is built stronger than the church:  argal,
the gallows may do well to thee.

Lady MacBeth
That which hath made them drunk hath made me bold;
What hath quench'd them hath given me fire.
     Hark!  Peace!
It was the owl that shriek'd, the fatal bellman ,
Which gives the stern'st good-night.  He is about it.

First Gaoler.  Come, sir, are you ready for death?

Posthumus.  Over-roasted rather; ready long ago.

First Gaoler:  Hanging is the word, sir:  if
you be ready for that, you are well cooked.

Posthumus.  So, if I prove a good repast to the
spectators, the dish pays the shot.

First Gaoler:
A heavy reckoning for you, sir.  But the comfort is,
you shall be called to no more payments, fear no
more tavern-bills; which are often the sadness of
parting, as the procuring of mirth:  you come in
flint for want of meat, depart reeling with too
much drink; sorry that you have paid too much, and
sorry that you are paid too much; purse and brain
both empty; the brain the heavier for being too
light, the purse too light, being drawn of
heaviness:  of this contradiction you shall now be
quit.  O, the charity of a penny cord!  It sums up
thousands in a trice:  you have no true debitor and
creditor but it; of what's past, is, and to come,
the discharge: your neck, sir, is pen, book and
counters; so the acquittance follows.

Posthumus.  I am merrier to die than thou art to live.

First Gaoler:
Indeed, sir, he that sleeps feels not the
tooth-ache:  but a man that were to sleep your
sleep, and a hangman to help him to bed, I think he
would change places with his officer; for, look you,
sir, you know not which way you shall go.

Posthumus.  Yes, indeed do I, fellow.

First Gaoler.
Your death has eyes in 's head then; I have not seen
him so pictured:  you must either be directed by
some that take upon them to know, or do take upon
yourself that which I am sure you do not know, or
jump the after inquiry on your own peril:  and how
you shall speed in your journey's end, I think you'll
never return to tell one.

Posthumus.
I tell thee, fellow, there are none want eyes to
direct them the way I am going, but such as wink and
will not use them.

First Gaoler.  What an infinite mock is this, that a man should
have the best use of eyes to see the way of
blindness!  I am sure hanging's the way of winking.

[Enter a Messenger.]

Messenger.  Knock off his manacles; bring your prisoner to the king.

Posthumus.  Thou bring'st good news; I am called to be made free.

First Gaoler.  I'll be hang'd then.

Posthumus.  Thou shalt be then freer than a gaoler; no bolts for the dead.

[Exeunt Posthumus Leonatus and Messenger.]

First Gaoler.
Unless a man would marry a gallows and beget young
gibbets, I never saw one so prone.  Yet, on my
conscience, there are verier knaves desire to live,
for all he be a Roman:  and there be some of them
too that die against their wills; so should I, if I
were one.  I would we were all of one mind, and one
mind good; O, there were desolation of gaolers and
gallowses!  I speak against my present profit, but
my wish hath a preferment in 't.

[Exeunt.]

[A ship containing a royal entourage is tossed about by a storm.  Responding to the gruff behavior of the Boatswain who tells them to keep out of the way, Gonzalo, a councilor, tries to cheer up the other passengers.]

Gonzalo.  I have great comfort from this fellow: methinks he hath no drowning
mark upon him; his complexion is perfect gallows.  Stand fast, good
Fate, to his hanging!  Make the rope of his destiny our cable, for
our own doth little advantage.  If he be not born to be hanged, our
case is miserable.

Note:  Gonzalo invokes a proverb that reads "He that is born to be hanged is in no danger of drowning."

[Later in the scene, Antonio shows his displeasure toward the Boatswain.]

Antonio.  We are merely cheated of our lives by drunkards.
This wide-chopped rascal!  Would thou mightst lie
   drowning
The washing of ten tides!

[See Execution Dock for an explanation of this passage.]