[Comments originally didn't work on this post; I've reposted it, and they work now.]
Shakespeare is often given credit for coining not just memorable phrases, but also hundreds of now-familiar words. The Christian Science Monitor (June 5, 2007), for instance, reports that "Shakespeare invented many words we still use today — such as amazement, lonely, and misplaced." Other sources cite still more, and the Oxford English Dictionary seems to support this judgment for many such words (including amazement, lonely, and misplaced, in at least some of their definitions). The New York Times (Dec. 26, 2004) echoed this view, though noted some uncertainty. The First Folio of Shakespeare, edited by Doug Moston and published in 1995, likewise reports that Shakespeare "actually invented over 1700 words which appear for the first time in his writing," including "accommodation, premeditation, assassination, submerged, exposure, frugal, generous, hurry, impartial, lonely, castigate, control, majestic, pious, sanctimonious, and obscene."
But the recent scanning of early English books in fully searchable format (see, for instance, Chadwyck-Healey's Early English Books Online [EEBO]) lets us test these claims — and it appears that many of them are mistaken: For instance, Philip Sidney's The Countesse of Pembrokes Arcadia (1590) contains the phrase "her coming to that lonely place (where she had no body but her parents)." Modern editions (for instance, here) seem to confirm that this corresponds to the modern English "lonely." The OED Shakespeare reference is to Coriolanus (1607).
Likewise, a publisher's note in Euclid's Elements (1570) contains the phrase — slamming the publisher's competition — "But of the disordring of it, can remayne no doubt, if ye consider in Zamberts translation, two other propositions going next before it, so farre misplaced, that where they are, word for word, before duSingle illegible letterly placed, being the 105. and 106. yet here (after the booke ended), they are repeated with the numbers of 116. and 117. proposition."
Shakespeare scholarship seems to be moving towards recognizing this: The RSC Shakespeare's William Shakespeare: Complete Works, edited by Jonathan Bate and Eric Rasmussen, puts it well (pp. xliv-xlv, paragraph beak added):
Shakespeare is sometimes said to have coined more new English words than anyone else, with the possible exception of James Joyce. This is not true. The illusion of his unique inventiveness in this regard was created by the tendency of the Oxford English Dictionary to cite examples from him as the first usage of a word. That was because of his ready availability when the dictionary was created at the end of the Victorian era. Now that there are large digitized databases of sixteenth-century books, it is easy to find prior occurrences for many supposed Shakespearean coinage.
Despite this, the list of neologisms remains impressive. To give a random selection of words, Shakespeare is responsible for such verbs [or at least for their use in the written language -EV] as "puke," "torture," "misquote," "gossip," "swagger, "blanket" ..., and "champion" .... [Note that some of these, such as "torture," are amply attested in noun form; Shakespeare is being credited here with verbifying them. -EV] He seems to have invented the nouns "critic," "mountaineer," "pageantry," and "eyeball," the adjectives "fashionable," "unreal," "bloodstained," "deafening," "majestic," and "domineering," and the adverbs "instinctively" and "obsequiously" in the sense of "behaving in the appropriate way to render obsequies for the dead" (only in the eighteenth century did the word come to connote "excessive deference" ...).
Let this be a reminder: (1) Be careful believing etymological claims, especially ones that sound especially cool, even if they occur in seemingly reputable sources. (2) Even if you check reputable sources, such as the Oxford English Dictionary, keep in mind their limitations — the OED doesn't, to my knowledge, claim that their earliest reference is proven to be the earliest printed use of a word, though it does tend to try to use the earliest reference it can find. (3) Finally, if you want to rely on claims like this, and you have a university account, see if you can do your own quickie research in databases such as EEBO and the like (which I understand many universities subscribe to).
Incidentally, I was going to also urge people to be careful in believing claims that some author "invented" a word: Authors rarely invent words, even using accepted rules of word formation — while new phrases often sound vivid and creative, new words generally just sound odd, especially when one gives a reader dozens in one work, unless one is self-consciously trying to create some sort of fictional dialect (as in A Clockwork Orange) or writing about new discoveries that require new technical terminology. But while I think this is generally good advice, I should note that UCLA English Prof. Robert Watson reports that English society was more open to invented words in Shakespeare's time.