Shakespeare's plays are as popular as they are because he was perhaps the greatest writer who has ever lived. It's partly because he was writing plays which go on being performed and therefore which can be brought freshly to life for each generation by actors of the present.
By 1610, the actors were performing Shakespeare in German as his plays had become popular in Danzig. Some of Shakespeare's work was performed in continental Europe during the 17th century, but it was not until the mid 18th century that it became widely known.
Not only did Shakespeare teach us about ourselves and humanity, but he also invented around 1700 words which we still use in everyday English today. He often changed nouns into verbs, verbs into adjectives, connecting words together and coming up with wholly original ones too.