No writer has had an influence as great as Shakespeare's. We quote him all the time without knowing it; there is a story that one reader complained "Hamlet" was full of clichés, because it contains (in fact, it invented) so many phrases still in use; "hoist with his own petard," "more in sorrow than in anger," "in my mind's eye," and many more.
As well as new metaphors and idioms, Shakespeare introduced new words. "Vast" and "horrid" first appeared in his work, as well as colourful (and usually insulting) phrases no longer in use, such as "three-inch fool" and "one-trunk-inheriting slave." Some of these were taken from his native Warwickshire dialect. The influence of this can be seen in the lines he gives to his "common" characters, like the shepherd's description of young men as "boiled-brains" in "A Winter's Tale," or the names for plants like "honeystalks" (white clover.)