Other than serious mental and physiological depression, especially marked after the death of his wife, Virginia, and alcoholism, the only indications that Poe was mentally ill came from a highly suspect source.
Rufus Griswold, a writer who hated Poe, somehow became his literary executor. The 'obituary' he wrote and the biography he later released used misconstruction, implication and outright lies to ruin Poe's posthumous reputation. It was many years before this became apparent, by which time it was firmly fixed in the public mind that Poe was insane.
I agree that there is no diagnosis of insanity, but I think a case could be made for bipolar disorder (aka manic depression). It seems that Poe had periods of enormous creativity followed by bottoming lows. He also had a habit of writing about the "double self," thus lending credence to the belief that he felt torn between two existences.
Some of his behavior was quite odd as well. I recall reading in his biography that when his wife (and 13 year old cousin) died, he had a strict ritual of walking around her grave a certain number of times each night, perhaps indicating OCD (obsessive-compulsive disorder.)
I don't think he was crazy, bi-polar maybe, and very depressed. The black cat, which is a short story he wrote, talks about a man who was very kind hearted and loved animals, but he became came an alcoholic, and turned very hostile. which is sort of bi-polar, because he was still the kind hearted man but also the alcoholic who cut out his cat's eye. Edgar Allen Poe was an Alcoholic as well.
But you see excessive drinking over a long time can cause serious problems with cognition and memory, as well as effect ones judgement. Alcohol can even cause exaggerated emotions, sadness for example. a lot of his poems and short stories deal with death, and are more sad than most poems.
So no I don't think he was crazy, I think that he suffered the affects of alcohol, causing depression, and possibly causing him to be bi-polar. I think writing reveals a lot about the author.
Anyway, hope that helped a little.