In the fall I will be teaching "Types of Literature," which explores the four traditional literary genres (drama, poetry, short story, novel). This requires a great variety of works, and while (in my opinion) requires one Shakespearian play, does not leave room for two of Shakespeare's plays if I wish to really explore the variety and potential of each genre.
The choices I have based on the anthologies available also happen to be my two favorites, and the two I would choose if given infinite choice: Hamlet and King Lear.
And right now I have no idea which to teach. I love teaching them both. Either would fulfill the objectives of the course. Both are culturally significant (though Hamlet moreso). Both are brilliant masterpieces. Both illuminate the nature of drama and tragedy. Both are rich thematically. Neither really facilitates easy discussion, but each is rich with big ideas and brilliant poetry. Hamlet allows me to show film versions, while Lear really does not.
Pedagogically, I'm leaning toward Hamlet, but on a personal level, I think I'd prefer King Lear.