Someone once said that every generation has its favorite Shakespeare play. Hamlet was a favorite with the Victorians. Macbeth enjoyed a great popularity in the first half of the 20th century; Othello in the second half. It seems to me that King Lear may be the play that will come to be associated with the early 21st century.
Whatever the general trend, Hamlet is always near the top of Shakespeare favorites.
As a result, quite apart from the famous “To be or not to be” and “What a work is man” soliloquies, many of the speeches, lines, and phrases have become embedded in our everyday speech. English speakers who have never read the play or seen it acted are likely to use one or more of the following expressions or some form or another:
To thine own self be true
Though this be madness, yet there is is method in ‘t.
The lady doth protest too much, methinks
In my mind’s eye
The play’s the thing
Frailty, thy name is woman!
Neither a borrower nor a lender be
to the manner born
Alas, poor Yorick!
Ay, there’s the rub
Brevity is the soul of wit
Conscience does make cowards of us all
Dog will have its day
Get thee to a nunnery
Hoist with his own petard
in my heart of hearts
It smells to heaven
murder most foul
Sweets to the sweet
Not a mouse stirring
something is rotten in the state of Denmark
Ahh, but here’s the rub…
How many of those phrases did Shakespeare actually invent?
Just because he wrote them in his plays doesn’t mean they weren’t in common usage beforehand (and remained so not because, but in spite of his works).
And my personal favorite (but less well-known): “I am but mad north-north-west: when the wind is southerly I know a hawk from a handsaw.”