As a revenge play, the universal of appeal to Hamlet is the expectation that those wronged will be avenged and those who committed the crime will come to some justice. What makes Hamlet more enduring than a typical revenge play is that Hamlet draws out the drama, hesitating at every turn because he must come to terms with the moral implications (for himself) of killing Claudius. Also, Hamlet wants to avenge his father and expose the sins of Claudius in the most dramatic way. As Hamlet feigns his madness, he manipulates other characters in such a way that it is as if he is trying to write the script of his revenge himself.
Also, Hamlet's internal conflict is philosophically profound. His "to be or not to be" speech is about whether it is more honorable (he says "noble") to live and try to carry out the revenge or to kill himself. It is a revenge play, but one with philosophical depth. For a contemporary analogy, Hamlet is like a typical big budget action movie or an intense suspense thriller, except the hero would consider the moral implications of each of his actions, and somehow the director would pull this off without losing any of the excitement or drama.