Genius is a subjective term, and although you'd be hard pushed to find somebody who doesn't think Shakespeare was a genius, it's also nearly impossible to define exactly why. One of the reasons, in my opinion, is that he resonates so profoundly with so many people through so many eras, the very reason his genius is so hard to pin down - you'd have to reconcile centuries of criticism and visceral reactions to his works to reach a vaguely accurate answer!
His longevity is a symptom of genius; his extraordinary reworkings of existing tales are too; the deft use of language to evoke emotions and ideas that barely existed in anyone else's mind let alone on the page or stage; mixing genres, confounding character types and levelling distinctions - all symptoms of his genius.
But what is it exactly that make the man a genius? I'm afraid I can't answer that, and I hold my hat up to the (wo)man who can.