When people talk about Shakespeare's contribution to the English language, they usually refer to the words he used. His works contain the first recorded use of many words, including bandit, dwindle, excellent and tranquil. That does not mean that he coined the words, just that no-one can find any written evidence of them before him. An academic from Strathclyde University has said that Shakespeare was no more inventive than his contemporaries when it came to vocabulary, but where he was really innovative was in the grammatical constructions he used. One example is his use of adjectives to describe inanimate objects; talking of horses and their "proud hoofs" was ground-breaking at the time.
Here's a Daily Telegraph article on the subject.