On the most basic level, we can sympathize with Gatsby for being a dreamer. He wanted something and he set out to get it. His desire, his passion...both deserve admiration and so his failures deserve (some) pity.
There is also a complex sort of powerlessness involved in Jay Gatsby's story. He wants to change. He wants to make himself into something that he thinks is better than what he once was.
This craving for betterment and change is naturally a sympathetic drive. We can all understand this impulse. Again, the fact that he fails in the end to achieve his aims might lead us to feel some pity for someone who had such a baldly sentimental goal.
In my opinion, Gatsby deserves our sympathy because he is an embodiment of the American dream, which is that we can remake ourselves, that there is equal opportunity to succeed, that here, no matter what a man's roots are, he can win the hand of a fair lady. In spite of the fact that Gatsby consorts with criminals, makes up stories about his past, engages in adulterous behavior, and has a dubious source of income, he has a naivete that appeals and a deeply romantic streak. At the end, it is his love for Daisy and his chivalry that kill him. He dies believing in the American dream.
The other aspect of Gatsby to bear in mind is the characters with whom we are comparing him. There is nothing appealing about the stupidity and brutality of Tom, the cynicism of Daisy, or the spectacularly unsuccessful social-climbing Wilsons. Passive Nick is not an engaging character, and neither is Jordan, who is almost immediately characterized as dishonest. Truly, Gatsby is a knight in shining armor in among this cast of characters.