By luck, as I was just finishing the novel, I was assigned Gatsby in my AP Literature class's Literary Death Match, aka a fight to the death. By this point I was basically in love with Gatsby, extraordinarily peeved at Daisy, and just detested Tom. I was a mess of feeling for this book and didn't do it justice.
But what I wanted to make a point of in the match against Frankenstein was why Gatsby was, indeed, great. After thinking about this central question a lot, I've come to the conclusion that Gastby was great because of his "extraordinary gift for hope," as Nick Carraway famously introduces him as possessing. Gatsby stares out across the bay, living on the wish of a perfect restoration of the past. All of the wealth and riches Gatsby acquires mean nothing if they do not please Daisy; he is only this rich because he wanted to meet her standards.
Gatsby is a perfect representation of the American dream: to become something out of nothing, to become wealthy in the monetary sense, but also in the sense that he would be rich having a "golden girl". But, perhaps because of the overwhelmingly wealthy lifestyle Daisy has lived her entire life has made her so careless, so unable to appreciate Gatsby. No matter Gatsby's endless waiting, Daisy just did not care, and this carelessness translates directly to the tragedy of the novel.
Gatsby was great because he is a manifestation of everyone's desire to live fully. His ambition is what we all have somewhere- Gatsby's was simply clouded by "foul dust floated in the wake of his dreams," or Daisy, the unworthy fixation of his devotion. Gatsby rose from nothing to almost unimaginably rich but the novel really is revealing how this wealth leads to corruption. The Great Gatsby is a perfect account of this life of Gatsby, who cannot be seen as anything less than great.