The web site No Sweat Shakespeare (linked in the resources section) has a long list of words that William Shakespeare is said to have coined, or at least to have been the first person to put in writing. In fact, the editors state that in all of his works combined, "Shakespeare uses 17,677 words: Of those, 1,700 were first used by Shakespeare." Among the words this site lists are gloomy, assassination, amazement, hurry, and suspicious.
Online Shakespeare (linked below) explains that Shakespeare created these new words "by changing nouns into verbs, changing verbs into adjectives, connecting words never before used together, adding prefixes and suffixes, and devising words wholly original." For instance, the word "blanket" is a noun, meaning a covering on a bed. But Shakespeare was the first writer to use it as a verb in Act II, scene 3, of King Lear, when Edgar says that he will "blanket my loins." We use the same verb form today when we say that the ground is blanketed in snow.
It could be that many of these words were in use in spoken language but were not considered proper to use in writing. Shakespeare used both formal and informal language in his plays because he depicts both noble and common characters. So it may be that he didn't invent these words but was the first to put them into print.