As far as teaching Hamlet goes, for me, this play is a text that contains at least one example of nearly every literary element. It is a fabulous text for an AP Literature student to have under his belt as it is complex enough to applicable to any kind of essay question that might come up on the exam.
Also, from a teaching perspective, this is a text that appeals to a very wide range of students (again, hard to find). It is typically taught to seniors because the most prominent themes are certainly appreciated by a more mature audience - but that is not to say that these themes are not appreciated by teenagers as well as adults. The book is appealing because the reader sympathizes with the melancholy, loneliness, and confusion of Hamlet. I also think about how many young men in my classes have been left fatherless - and have assumed the "man of the house" role at very young ages. Despite that Hamlet is a rich white kid and many of these students are not - I see that they connect to the book in a deeper way than others.
Girls love this book because they understand how Ophelia feels when Hamlet starts going crazy. And for those students who catch the humor - Hamlet is a funny play.
Many critics consider Hamlet to be the first "modern" character, in that he steps outside the boundaries of his role as tragic hero, to really consider the question of what it means to be a human being and take action in the world.
Philosophically, there have been many movements and approaches to living our human lives, but Hamlet seems to be a character who could be considered pertinent to them all. Even one of the most modern philosophies, Existentialism, which questions the meaning and purpose behind human action, seems to apply.
Theatrically, the character itself is considered the greatest acting challenge for an English speaking actor. And an explanation for this could be that Hamlet does not really exist separately from the actor who plays him. The great and memorable Hamlets have each found and shared some unique aspect of the role, an aspect that each has found inside him/herself.
Hamlet, whether considered as a juicy role for an actor or as a mirror in which audience members see themselves, is still popular largely because he embodies the question: "What does it mean to be a human being?"
Shakespeare was a master of both literature and art but also an inspired soul when it came to making history a story masterpiece. His works have remained some of the most substantial and important pieces of literature. His writing tells us about what his times were like, life, food, style and laws. It gives us knowledge regarding existence at that particular time period. Shakespeare is regarded as a literary instructor, what with his use of old english and his sonnets that forever remain.