Revenge
The idea of exacting revenge for a crime is (fairly) foreign to modern society; we have to think of something quite outside the law to come up with an equivalent. West Side Story sets Romeo and Juliet in the context of New York gangs, but in Hamlet the role of kingship is too powerful, too responsible, for gangland to be an effective analogy.
The conflict between the law and direct revenge that we perceive was less clear in Shakespeare's time, as the attitude to duelling attests; but Hamlet was faced with possibly a deeper conflict: between the Christian teachings of patience and turning the other cheek; and the ancient desire for blood revenge.