"The Tell-Tale Heart" is still widely read today, because it is such a great story. It has a fascinating narrator who confesses to murder right off the bat-that is a great hook to get people interested. Then his description of the eye, the waiting in the dark, the horror of the old man, the audacity of placing the police right above the body, the beating heart, and the gushing confession...all are just so well-writtng, suspenseful, and intense. So, it is, at its core, just a great story.
Another reason that it is still widely read today is that it is relatively short and easy to understand; this is a great asset when teaching short stories, and helps students to keep their attention focused the entire time, and to comprehend it.
One last reason that it is still widely read today is that in recent years, the horror/suspense genre has taken off. It has become really, really popular. Just look at all of the horror movies that come out every month; people like horror, especially these days. So, that is another reason it is read today-its genre fits a popular style.
I hope that those thoughts help! Good luck!