Shakespeare has had an enormous influence on English literature. Shakespeare, who was never afraid to innovate, contributed more than 1,700 words to the English language. More importantly, he innovated with character. For example, Hamlet has been called the first modern play because of the intense interiority of its title character. Hamlet is always thinking, and the audience is allowed to hear those thoughts through his many soliloquies.
Because Shakespeare had a deep understanding of people from all walks of life and created deeply imagined, well-rounded characters, so human they can seem nonfictional, the subjects of his plays sank deeply into the psyches of many great writers, as well as into the hearts of anyone else who experienced his work. His plots were also very well known, and by the late eighteenth century, he was revered even though he broke all the rules of Classical drama. Thus, writers frequently allude to him, to the point that unfamiliarity with Shakespeare can rob readers of much of the allusive richness of English literature.
A contemporary parallel to Shakespeare's influence would be The Wizard of Oz. This work has so permeated the American consciousness that most Americans understand immediately what such allusions as "we're not in Kansas anymore" or "the witch is dead" mean without needing them explained or told where they come from.
Likewise, allusions to Shakespeare show up everywhere in English literature, high literature and low. For example, in Jane Austen's Emma, considered one of the great novels in English, Emma quotes A Midsummer's Night Dream. In popular literature, Agatha Christie's mysteries, such as Something Wicked This Way Comes, allude to Shakespeare. One could make a pastime of locating Shakespeare allusions in English literature and find them all over.