Not by Shakespeare, but from Finding Your Strength in Difficult Times: A Book of Meditations, a 1993 self-help book by David S. Viscott.
Misattributed
Source: http://quoteinvestigator.com/2014/06/16/purpose-gift/

“Down, down to hell; and say I sent thee thither.”

William Shakespeare Henry VI (play) Part 1-3

Richard of Gloucester, Act V, scene vi.
Henry VI, Part 3 (1592)

“Golden lads and girls all must,
As chimney-sweepers, come to dust.”

William Shakespeare Cymbeline

Guiderius, Act IV, scene ii.
Cymbeline (1610)

“We have seen better days.”

William Shakespeare Timon of Athens

Flavius, Act IV, scene ii.
Timon of Athens (1605)

“Crabbed age and youth cannot live together:
Youth is full of pleasure, age is full of care”

William Shakespeare book The Passionate Pilgrim

The Passionate Pilgrim: A Madrigal; there is some doubt about the authorship of this.

“The fox barks not, when he would steal the lamb.”

William Shakespeare Henry VI (play) Part 1-3

Suffolk, Act III, scene i.
Henry VI, Part 2 (1592)

“I gyve unto my wief my second best bed with the furniture”

William Shakespeare

Shakespeare's will

“Beware the leader who bangs the drums of war in order to whip the citizenry into a patriotic fervor, for patriotism is indeed a double-edged sword. The saying goes you live by the sword you shall die by the sword…It both emboldens the blood, just as it narrows the mind. And when the drums of war have reached a fever pitch and the blood boils with hate and the mind has closed, the leader will have no need in seizing the rights of the citizenry. Rather, the citizenry, infused with fear and blinded by patriotism, will offer up all of their rights unto the leader and gladly so. How do I know? For this is what I have done. And I am Caesar.”

William Shakespeare

This statement by an unknown author has also been wrongly attributed to Julius Caesar, as well as to Shakespeare's play on his assassination and its aftermath, but there are no records of it prior to late 2000. It has been debunked at Snopes.com http://www.snopes.com/quotes/caesar.htm <br class="br">Misattributed

“Full fathom five thy father lies;
Of his bones are coral made;
Those are pearls that were his eyes;
Nothing of him that doth fade,
But doth suffer a sea-change
Into something rich and strange.”

William Shakespeare The Tempest

Ariel, Act I, scene ii.
The Tempest (1611)

“He who has injured thee was either stronger or weaker than thee. If weaker, spare him; if stronger, spare thyself.”

William Shakespeare

Truly from Seneca the Younger, in De Ira, Book III, Chapter V:
Aut potentior te aut inbecillior laesit: si inbecillior, parce illi, si potentior, tibi.
Misattributed

“Nothing is more common than the wish to be remarkable.”

William Shakespeare

Oliver Wendell Holmes, Sr., The Autocrat of the Breakfast Table (1858), ch. XII : Nothing is so common-place as to wish to be remarkable.
Misattributed
Source: https://en.wikiquote.org/wiki/Criminal_Minds_(season_1) Criminal Minds] ("L.D.S.K." - season 1, episode 6).