With all due respect to the previous responder, I do think that Gatsby had a kind of greatness. He invented himself, essentially, and was idealistic enough to buy into the American Dream. His love for Daisy was courtly and idealistic, too. He protects Daisy, as her husband is unlikely to have done, and this is what leads to his death. The last time Nick speaks to Gatsby, he walks away and then turns around to say,
They're a rotten crowd....You're worth the whole damn bunch put together (162).
Nick is certainly conflicted about Gatsby, because he goes on to say he "disapproved of him from beginning to end (162). Nevertheless, throughout the entire book, he does find admirable qualitites in Gatsby, and he cannot help but express this at the end.
Two meanings of the word great are unusual or considerable in degree; being such in an extreme degree. Certainly Jay Gatsby aspired to greatness in love, greatness in wealth and personal possessions: He follows the green light of the American Dream. And, while his dream is illusionary, his efforts are, indeed, great. In fact, is the realization of the aspirations and tremendous drive of Jay Gatsby to rise in society that leads Nick to admiringly tell Jay, "You're worth the whole damn bunch put together"; at least, Jay Gatsby is genuine in his desires--although his goal is false--unlike the others that attend the parties at West Egg.
In addition, this title, "The Great Gatsby" conjures the introductions made at a circus (e.g. The Great Gambini, a daredevil on the trapeze.) Within the small world, the make-believe world, of the circus, a performer may be great. However, in the scope of the world, the greatness is clearly mitigated. Similarly, Gatsby's greatness is ironic; in the scope of the decadence and falseness of the Jazz Age, it is showy and cheap, and does not reach true value.
First of all, Fitzgerald did not want to call the novel "The Great Gatsby." So maybe he did not see Gatsby as all that great.
I guess I think of it as an ironic title. Gatsby seems great in the sense that he is really important and well-liked during his lifetime. So the word "great" appears to refer to his standing in society. But he only seems this way. In reality, he is a very lonely guy who does not have any real friends.
When he is murdered, essentially no one comes to Gatsby's funeral. This shows that his "greatness" was illusory.