I do have sympathy for Gatsby, but only to a certain extent. I think he is a pathetic character. He wants what he can't have. I feel sorry for him because people will never take him seriously.
I sympathize with Gatsby on a number of levels, but perhaps the main one is his naivety. Despite everything that he has been through in his life, he is still an idealist, so much so that he refuses to see the bad in people. He is very boyish, and not just around Daisy. When I analyze my feelings about Gatsby, I always come back to the scene where Tom and his friends stop at Gatsby's on their ride--how excited Gatsby is when the lady invites him to dinner, and then how incredulous and rude the group is when Gatsby goes inside to collect his things. I think most people have been the brunt of others' superficiality, and, therefore, most can feel a pang of embarrassment for Gatsby in this scene.
I think he's sympathetic to many people because he is a recognizable American archetype-- the kid who came from nothing and got everything. He's also sympathetic because he's the type of person who sets out certain goals, achieves them, but is still left wanting. His insecurity coupled with his success is something a lot of people relate to or find sympathetic I think.