The question of whether or not Gollum is a sympathetic character is a hard one; after all, he does murder Deagol for the One Ring, not to mention all of the other things he does to Bilbo and Frodo. However, I think that yes, Gollum is a sympathetic character. Before he found the One Ring, Gollum was known by his real name, Smeagol, and he was one of the Stoors, one of the three earliest types of Hobbits (he was later known as Gollum because that was the sound he made when he coughed). He was a peaceful creature until the One Ring came into his life, urging him to murder Deagol, his own cousin, in order to get it from him as a "birthday present," which is how he later refers to the Ring. All of the terrible things he does can be blamed on the influence of the Ring. As a powerful, evil object that holds the malice of its maker, Sauron, the Ring exerts power over its bearer, making them do things that they would not normally do. So despite all the terrible things Gollum does, it is not truly his fault--the Ring is to blame, and the terrible influence it has on him--so he is seen as a "bad guy" and in the end he dies because of the Ring.