Jay Gatsby is great because his reach exceeded his means, because his dream was what drove him, because he did not accept failure, because he saw the world as a place of possibility, not a place of limits.
He was not great because he was a liar, a cheat, and a snob. He succeeded in re-creating himself but did so by lying to everyone - including himself. There was no point in his story when he admitted the moral ambiguity of his situation. This is alarming when we consider his adultery and the way he made his money.
Gatsby is great because, as we learn in the last chapter, he had big dreams for his life long before he met and fell in love with Daisy. His childhood notes reveal his "moral perfection" list, and we see that he lived much of his life in attainment of those goals. Where he is not great is in his losing sight of the fact that he had a vision of his life that was rather pure and it was corrupted by his love for Daisy. The personal goals became entwined with what he thought he needed to get her, and he lost his way.
I think that the title is ironic. I think that he's not great. The reason for that is the fact that he's pathetically trying to chase this illusion. He thinks that he can buy love. That's really sad. He's gone to all these lengths (including breaking the law) to pursue something that he really can't have and that isn't that admirable. So I don't really think he's great at all.
Gatsby was great because he had a dream; he put everything he had into attaining that dream and he got it...for awhile. He was also charming and loyal which are wonderful qualities, but they allowed him to be used by other selfish people.
Gatsby fell in love with Daisy when he was a poor soldier. When he went off to war, she got tired of waiting and got swept up into the fast world of money and status and wealthy Tom Buchanan took her there. She eventually married Tom, as Gatsby found out when he returned.
He could have let that setback destroy him, but instead he went to work finding a way to get her back. He watched the world around him and learned how to make money. He made so much money that he was able to buy a house close to Daisy's and lure her back into his world and arms by throwing lavish parties.
Daisy was his own, for awhile, because Gatsby did what he had to do to get what he wanted. What he couldn't have known was that Daisy was never motivated by love, but strictly by status and money.
He was so loyal to Daisy that he took the rap for her when she hit and killed Myrtle which ultimatly caused his own death.
What isn't so great about Gatsby is that he went about getting his money illegally (most likely through bootlegging). He also had an affair with another man's wife which is not a very admirable quality.
He had many women.