Shakespeare's plays have not changed over time; it is more that people sometimes seek to change them. They are so often performed that directors may choose to interpret them or present them in different ways. So you might have the play set in modern times, the sets totally different from in shakespeare's own. Or another director may set the play in a distant country.
In Shakespeare's time the plays were acted 'in the round' with the audience milling around the action, not sitting at a distance on seats in the dark. Now the plays may be outdoors in the grounds of a stately home. The strength of the work is that it can adapt and hold serious meaning to audiences experiencing them in different ways. The essence of each play remains the same.