There is a book about the subject called Coined by Shakespeare: Words and Meanings First Penned by the Bard by Stanley Malless and Jeffrey McQuain. If you would like a taste of the words he introduced to the English language, here is a brief list:
accused, addiction, alligator, amazement, anchovies, assassination, backing, bandit, bedroom, bump, buzzers, courtship, critic, dauntless, dawn, design, dickens, discontent, embrace, employer, engagements, excitements, exposure, eyeball, fixture, futurity, glow, gust, hint, immediacy, investments, kickshaws, leapfrog, luggage, manager, mimic, misgiving, mountaineer, ode, outbreak, pageantry, pedant, perusal, questioning, reinforcement, retirement, roadway, rumination, savagery, scuffles, shudders, switch, tardiness, transcendence, urging, watchdog, wormhole, zany
besmirch, bet, blanket, cake, cater, champion, compromise, cow, denote, deracinate, dialogue, dislocate, divest, drug, dwindle, elbow, enmesh, film, forward, gossip, grovel, hobnob, humour, hurry, impedes, jet, jig, label, lapse, lower, misquote, negotiate, numb, pander, partner, petition, puke, rant, reword, secure, submerge, swagger, torture, unclog
aerial, auspicious, baseless, beached, bloodstained, blushing, circumstantial, consanguineous, deafening, disgraceful, domineering, enrapt, epileptic, equivocal, eventful, fashionable, foregone, frugal, generous, gloomy, gnarled, hush, inaudible, invulnerable, jaded, juiced, lackluster, laughable, lonely, lustrous, madcap, majestic, marketable, monumental, nervy, noiseless, oscene, olympian, premeditated, promethean, quarrelsome, radiance, rancorous, reclusive, remorseless, rival, sacrificial, sanctimonious, softhearted, splitting, stealthy, traditional, tranquil, unmitigated, unreal, varied, vaulting, viewless, widowed, worthless, yelping
importantly, instinctively, obsequiously, threateningly, tightly, trippingly, unaware
There are so many words on that list that it just amazes me. How did they even speak without these words?