Spoon's list of some common words which were invented* by Shakespeare

accommodation, aerial, amazement, apostrophe, gnarled, hurry, impartial, inauspicious, assassination, auspicious, baseless, bump, castigate, changeful, clangour, countless, courtship, critic, dexterously, dishearten, dislocate, dwindle, eventful, exposure, fitful, frugal, generous, indistinguishable, invulnerable, lapse, laughable, lonely, majestic, misplaced, monumental, obscene, perusal, pious, premeditated, radiance, reliance, road, sanctimonious, seamy, sportive, submerge.
 
Spoon's follow up list of common phrases which were created* by Shakespeare
barefaced, fancy-free, green eyed, heartsick, hot-blooded, housekeeping, lacklustre, leapfrog, long-haired, pitched battle, clothes make the man, method in his madness, to thine own self be true, towering passion, ministering angel, every dog will have his day, frailty thy name is woman, neither a borrower nor a lender be, brevity is the soul of wit, mind's eye, primrose path, flaming youth, it smells to heaven, the lady doth protest too much, it's Greek to me, live long day, breathe one's last, heart of gold, give the devil his due, too much of a good thing, naked truth, foregone conclusion, break the ice, strange bedfellows, wear one's heart on one's sleeve, all that glitters isn't gold, eat out of house and home, be all and end all, more sinned against than sinning, one fell swoop, the milk of human kindness, the course of true love never did run smooth.
 
*Spoon's caveat in all things Shakespearean
Since we know so little for certain about a man that everyone has heard of, these lists contain words and phrases either invented by Shakespeare or in use at the time and written down for the first time by him. Or his are the oldest surviving texts to feature them. One of the above at least.