Here is a selection of phrases coined by Shakespeare:

Bated breath (The Merchant of Venice)
To be-all and the end-all (Macbeth)
To beggar description (Antony and Cleopatra)
We have seen better days (As You Like It)
A blinking idiot (The Merchant of Venice)
Brave new world (The Tempest)
Brevity is the soul of wit (Hamlet)
Cruel to be kind (Hamlet)
A dish fit for the Gods (Julius Caesar)
He hath eaten me out of house and home (Henry IV Part 2)
Foregone conclusion (Othello)
Laid on with a trowel (As You Like It)
Neither rhyme nor reason (The Comedy of Errors)
Short shrift (Richard III)
Sterner stuff (Julius Caesar)
Too much of a good thing (As You Like It)
A tower of strength (Richard III)
Wild-goose chase (Romeo and Juliet)