To speak of Shakespeare's legacy is to embark on a huge topic, far bigger than a short post can handle. So, let me mention only a few points.
First, Shakespeare has left behind many works. He is one of the most prolific and famous writers in all of the English language. He is still very much alive today and still incredibly famous. From high school students to professionals, we still act out the plays.
Second, he, as a word smith, has influenced our language and vocabulary. For instance, if someone uses the expression, "bated breadth," then they are using something from Shakespeare's Merchant of Venice." Another example is an expression from Othello,"foregone conclusion."
Third, he has shaped our imagination as his works have seeped into our culture and society. Moreover, his penetrating analysis of human nature is still very much with us today.