Other than making some great phrases and creative insults, two contributions come immediately to mind.
His first contribution would be the sonnet form he used. Sonnets originated in Italy and were popularized by poet Francesco Petrarca, more commonly known as Petrarch, and were initially brought to England by Sir Thomas Wyatt and Henry Howard, Earl of Surrey. Though they both had translated Petrarch’s sonnets, Wyatt used the form in his own original work.
The problem is Petrarchan sonnets, as a form, are more suited to a romance language like Italian. The rhyme scheme is abbaabbacdcdcd and is difficult for a germanic language like English.
Shakespeare used the form ababcdcdefefgg. This rhyme scheme was much easier and was used by other famous poets such as Charlotte Smith, William Wordsworth and Samuel Taylor Coleridge.
Shakespeare also added many words to the English language. "Bedroom" first appeared in 1600 in Act II Scene ii of Midsummer Night’s Dream, "bloodstained" in 1594 in Act II Scene iii of Titus Andronicus, and the list goes on. Where these were likely words he may have overheard, they were not put into print until the manuscripts were all together in the 1623 quarto.
For more information on his wordplay, see Shakespeare’s Wordplay.