Sméagol lived east of the Misty Mountains in the ancient, ancestral river valley homeland of the Stoorish Hobbits. There, Sméagol often fished and explored with his cousin Deagol. One day—on Sméagol's birthday, coincidentally—Deagol discovered the One Ring at the bottom of a river whilst fishing. Manipulated by the powerful will of the Ring, Sméagol murdered his cousin and kept the Ring for himself. Afterwards, upon discovering the Ring's effect of making the wearer invisible, he terrorized his home town, stealing and murdering until he eventually fled to hide in the roots of the Misty Mountains.
Sméagol is known as 'Gollum' in The Hobbit, as that is the peculiar guttural sound he made. Gollum is a name for Sméagol's mischievous and evil side, as he often verbalizes his internal struggles between the powerful draw of the Ring and his loyalty to Frodo, the final Ringbearer. Sméagol/Gollum has appeared in The Hobbit and The Lord of the Rings, and plays a very important role.
Tolkien's characters have many correlations to obscure words and cultures; he greatly enjoyed playing with words and names in a variety of languages. The name 'Sméagol' comes from the Old English word Smial--pronounced "Smile"---which means 'burrow.' It also comes from the Old English word 'Smygel,' which means "burrowing," or "worming in." This fits Sméagol/Gollum's character perfectly, as he is often portrayed as sneaky or deceitful. He has also lived for years underground in the caves of the Misty Mountains, never seeing the sun. Very worm-like indeed.
The name of Sméagol's cousin Deagol also bears significance: the English word "Dial" means "secret," and the Old English word "dygel," the origin of Deagol, means 'hiding away.' Thus, Deagol's name literally meant 'secret,' which is very appropriate as Deagol was Gollum's secret.
Tolkien's intricate web of plots and words are clearly what makes him one of the greatest writers of all time.
See also: Gollum, The Hobbit, Lord of the Rings.