Based on "The Tell-Tale Heart," why does Poe continue to have a hold on the American imagination?

This is a very open-ended question, but I think what you are getting at is this:  what techniques does Poe use in this particular story that make him such a fixture in American literature.

First of all, in this story and in "Cask of Amontillado", Poe champions the unreliable narrator.  Although using the first-person narrator was not unusual, most narrator's in the Romantic era were truthful and reliable.  Poe creates the "disturbed" narrator, one that readers can both emphathize with and yet mistrust.  The narrator in "Tell-Tale" is a murderer, despite all his rationalizations.  We can see that in the first paragraph as he tries to convince us that he isn't insane - his nervous manner clearly indicates that he is.   Then, when he is discussing the imagined sound of the heart beating between the floors, we see that his senses can't be relied upon:

And still the men chatted pleasantly, and smiled. Was it possible they heard not? Almighty God!—no, no! They heard!—they suspected!—they knew!—they were making a mockery of my horror!-

As readers, we are drawn in by the internal struggle being portrayed.  The pleasantly chatting men prove to us that this sound is unheard.  But we know that our murderer is losing his grip and becoming overwhelmed by it.  Will he be caught?  How will it happen?

The beauty of Poe is how well he crafts this crazy man.  If he was not experiencing this struggle of conscience, we might not enjoy the story so much.  He would simply be a villian to dismiss.  But the long process of rationalization shows us that this is a man who believes he has done the world a favor.  That struggle is part of why he is so capitivating a character, for all of us have been obsessed and bothered by a tiny detail at some point in our life - so there is a feeling of identification for readers, and of fear.  Could we become him?

Remember, too, that Poe was one of the first authors to delve into the heart (excuse the pun!) of a criminal.  Like all artists that "did it first", we remember him most.  He creates the effect of suspense by keeping the length of the story short enough to enjoy in one quick sitting.  He uses the internal monologue to help us identify with the narrator.  He surprises us with the climatic end moment.  He is a master!