Although many of the characters in The Hobbit are seen again in The Lord of the Rings, a small introduction for the main characters is necessary. I've limited this severely because otherwise I would be writing an encylopedia. Also rather than regurgitate the plot for each character there are small snippets of interesting factoids.
Bilbo is a hobbit who lives in Bag End, a hobbit hole in The Shire. Hobbits are also known as Halflings, an ancient mortal race. Bilbo is the son of Bungo Baggins and Belladonna Took. Bilbo is 50 when he sets off with Gandalf, Thorin and the rest of the dwarves. For this adventure please see the plot summary tab. Later adventures of Bilbo's are detailed in The Lord of the Rings trilogy.
Bilbo is most well-known for finding (or stealing) the One Ring of Sauron from Gollum. This occurred under the Misty Mountains as Bilbo was escaping from the goblins. He passed the ring on to his nephew Frodo at his eleventy-first birthday party, and Frodo eventually destroyed the ring in Mount Doom (the chronicles of this adventure are detailed in The Lord of the Rings).
Bilbo worked on his memoirs, which are known as the Red Book of Westmarch. As he had technically been a ring-bearer he was allowed to take the final journey to the Undying Lands with Frodo and the Elves.
Gandalf the Grey
Gandalf is a wizard (or Istar) sent by the West in the Third Age to combat Sauron. He is also known as Gandalf the White.
Gandalf spent time in The Shire, dwelling among Hobbits, and amusing them with his legendary fireworks. He was good friends with Bilbo's Took grandfather. He sets in motion the quest to regain the Lonely Mountain from Smaug, and also plays a large part in the Fellowship of the Ring and in the subsequent events.
During the journey to the Lonely Mountain Gandlaf finds his sword, Glamdring, in a weapons cache after killing the trolls guarding it. He is also deeply troubled by two things during The Hobbit; one being Bilbo's possession of the One Ring, and the second being the resurgence of a being he believes to be Sauron (called The Necromancer in The Hobbit).
Thorin, son of Thrain, is called Oakenshield because he used an oaken branch as a shield at the battle at the East-Gate of Moria. He became King-in-Exile of Durin's folk (dwarves) after his grandfather died and his father disappeared.
Thorin's greed overwhelmed him after the death of Smaug, and he refused recompense to the Men or Elves that asked. This eventually lead to the Battle of the Five Armies, during which Thorin was killed.
His last words were: "If more of us valued food and cheer and song above hoarded gold, it would be a merrier world. But, sad or merry, I must leave it now. Farewell." (Tolkein, 346-7).
Orignally known as Smeagal, Gollum is taken over by his desire for the One Ring. He is key in passing the ring on to Bilbo (who in turn passes it to Frodo and it is eventually destroyed), and guiding Frodo and Sam through Mordor in The Lord of the Rings. He was a Stoor, a Hobbit-like people.
Gollum lived under the Misty Mountains for hundreds of years before Bilbo met him, and lived off raw fish. He developed a type of split personality, where Smeagol was the 'good' personality and Gollum was 'evil'. He called the ring his 'precious(ssss)' and coveted it above all else.
Smaug is a fire drake of the Third Age who was drawn to the immense treasure trove the dwarves held in the Kingdom of Eredor. Smaug held the Lonely Mountain, after driving out the dwarves, for nearly 200 years. He was killed by an arrow shot by Bard the Bowman, a lord of nearby Laketown.