Be it an essay or a project, any written piece of work gets enriched with the addition of a quote. So familiarise your children with the work of the Bard and help make them intellectually inclined. Encourage them to memorise these most famous and widely used of Shakespeare quotes, so they can use them whenever possible. Some of these quotes can be used by younger children, while others would be better understood by teens. Read on, and commit a few of these quotes to memory. Use them in your daily life, thus exposing your children to the wonderful world of literature. You don't have to be an M.A. in English to do this. All it takes is a little perseverance, a little reading and a little memorising. 
 

Hamlet

Neither a borrower nor a lender be; 
For loan oft loses both itself and friend, 
(Don't borrow or lend money, or you may lose both the money and the friend.)

Frailty, thy name is woman!
(This quote signifies betrayal by a woman.)

Brevity is the soul of wit.
(Be brief while speaking, if you want to be witty.)

To thine own self be true
(Be true to yourself - only then can you be true to others.)

To be, or not to be: that is the question:

Thus conscience does make cowards of us all;
(Our conscience - and the consequent fear of the hereafter - prevents us from taking certain actions, thus turning us into cowards.)

Rich gifts wax poor when givers prove unkind.
(An expensive gift given by an unkind person loses its charm.)

When sorrows come, they come not single spies, 
But in battalions.
(Tragic events seem to come together, all at once.)

One may smile, and smile, and be a villain. 
 

Romeo and Juliet

What's in a name? That which we call a rose
By any other word would smell as sweet.
(A name is not important.)

Wisely and slow; they stumble that run fast.
(Similar to 'Slow and steady wins the race.')
 

Twelfth Night

Be not afraid of greatness: some
are born great, some achieve greatness, and some
have greatness thrust upon 'em.

If music be the food of love, play on;
Give me excess of it, that, surfeiting,
The appetite may sicken, and so die.
(When a person is given excess of a certain thing, he loses his desire for it.)
 

As You Like It

How bitter a thing it is to look into happiness through another man's eyes! 
(Envy: We are rarely truly happy at another man's success.)

All the world's a stage,
And all the men and women merely players.
(The world is a stage, and people are actors playing a part.)

Time is the justice that examines all offenders.
(Everyone gets their due with time. A wrong deed will not go unpunished.)
 

All's Well That Ends Well

Love all, trust a few
Do wrong to none:

Our remedies oft in ourselves do lie.
(This line signifies a rejection of fate. We are responsible for our future.)

All's well that ends well:
 

Othello

How poor are they that have not patience!
What wound did ever heal but by degrees?
(Those who don't have patience are poor. Even a wound heals slowly.)
 

The Winter's Tale

What's gone and what's past help
Should be past grief
(If you have lost something, and there is nothing you can do to get it back, there is no point in getting upset or grieving about it.)
 

The Merchant of Venice

All that glisters is not gold.
(Similar to "Don't judge a book by its cover." Things aren't what they appear to be.)
 

Julius Caesar

Et tu, Brute? Then fall, Caesar
(This is one of the most popular lines of this play, and it signifies betrayal of a close friend.)
 

Measure for Measure

Our doubts are traitors and make us lose the good we might win, by fearing to attempt.
 

King Lear

How sharper than a serpent's tooth it is to have a thankless child! 
(A thankless child that does not love her parents causes them tremendous grief.)

Nothing can come of nothing.
(Effort: If you want something, you have to put in effort. If you don't, you will get nothing.)
 

Much Ado About Nothing

There's not one wise man among twenty will praise himself.
(Fools praise themselves. Wise men are modest.)