Gollum was originally a creature of Hobbit-like origin known as Sméagol. He and his cousin Déagol discovered the One Ring at the bottom of a river. Already affected by the Ring's influence, Sméagol killed his cousin for it, justifying it by telling himself that it was a birthday present from Déagol.
Bilbo Baggins came across Sméagol beneath the Misty Mountains, although Bilbo thought of this creature as "Gollum" due to the yucky coughing noise Sméagol now made. He had lived alone with the Ring for centuries, and developed two separate personalities, which held conversations with each other. Ignorant of the Ring's significance to Gollum, Bilbo finds it on the floor and takes it.
Bilbo and Gollum had a riddle contest, with Bilbo set to become dinner if he lost. Bilbo cheated to win ("What have I got in my pocket?"), and Gollum cheated right back, planning to turn invisible with the Ring and eat Bilbo anyway. When Gollum found the Ring missing, he realized exactly what "that nassssty Bagginses" had in his pocket. Fortunately, Bilbo discovered the Ring's power in time to escape, and spared Gollum's life.
Gollum led them all the way to Cirith Ungol, where he tried to get the Hobbits eaten by Shelob. They escaped, and reached Mount Doom on their own. Frodo was finally overcome by the Ring and refused to destroy it, but Gollum made a successful last-minute attack for the Ring. As a result, Gollum toppled into the Cracks of Doom, destroying both the One Ring and Sauron.
Gollum's very existence tends to be ignored by most Tenth Walker Sues. This isn't surprising, considering Gollum's appearance, behavior, and lack of plot involvement during the early parts of The Lord of the Rings. When he is acknowledged in the Mines of Moria, the OC is likely to steal Gandalf's lines about him. Fifteenth Walkers will potentially accompany Bilbo to Gollum's cave, and potentially muck that scene up beyond recognition. (The One Ring can only turn one person invisible at a time, after all.)
Gollum even occasionally gets slashed with one of the Hobbits with whom he traveled into Mordor. This is usually with Frodo, since Sam was much less trusting of Gollum. Either way, you probably need to go here now.