It wasn't really a movie so much as anthology of Poe's short stories -- The Tell-Tale Heart, The Raven, The Pit and the Pendulum, and The Cask of Amontillado -- performed as one-handers by Vincent Price, but they really were wonderful examples of dramatic readings:
"The Bells" sort of does have a story - I was fairly convinced once reading an analysis that claimed it "rang" of four stages of life.
But, to your point: I think my favorite Poe movie would have to be the version of "The Premature Burial" by Roger Corman (incidentally, the only Corman/Poe movie without Vincent Price). It's not necessarily a perfect adaptation of the story, but I think it retains that spirit of Poe (like you said). I also did like the independent film "The Death of Poe" by Mark Redfield out of Baltimore. It's a pretty interesting theory on Poe's final days. If you haven't seen it, look it up and order it online.
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It was night in the lonesome October, of my most immemorial year.
The problem with adapting Poe's works to movies has always been that the stories are too short to support an entire movie, so a lot has to be added to fill in the story I like The Raven (1935) with Bela Lugosi because it doesn't try to adapt a Poe story; it just uses Poe as a theme to propel the plot. I also like The Tomb of Ligeia with Vincent Price. On the DVD there is a commentary by Roger Corman. He admits he was getting a little bored with his own Poe movies, and with that one, he tried to break his own formula as much as he could. I just saw a silent movie called The Bells that is supposed to be inspired by Poe's poem, with Boris Karloff and Lionel Barrymore. Obviously, the poem doesn't have a story, but it is a pretty weird psychologically based movie.