Both Frodo & Smigel aka Gollum are possessed by the ring since they have both worn the ring. Frodo shows his wisdom as a merciful and kind Hobbit. He shows bravery to go against popular opprobrium by saving this miserable creature from sure death. He also knows that although a loathing creature that he is, Gollum was to prove invaluable later on as he did save Sam & Frodo's lives when they were at the gateway when all the evil troops were emerging, he had the foresight to have the Hobbits duck for cover. Gollum also knew the alternative path inside. Gollum died because of his lust for the ring at his end & this is the one oversight Frodo didn't factor in.

Ok; this is entirely speculation on my part, but having read the books a dozen or so times I do think I have something to say. It is my belief that Frodo kept Smigel around because he needed to. Bilbo held the ring and became corrupted by it. Smigel was much more corrupted, and Frodo himself began to feel the power and corruption of the ring. Frodo kept Smigel around because he needed to believe that the corruption was not permanent. If he accepted that Smigel was beyond redemption, this meant that both he and Bilbo were also beyond redemption. For Frodo, Smigel was the physical manifestation of hope.

This is explained more fully in the books. Frodo himself has experienced the effects of the ring, and used it. Through these experiences he has gained more spiritual insight into the matter, and can now pity Gollum, seeing the horrible way Gollum has become a slave to it. He now understands Gandalf's earlier remark, that it was pity that stayed Bilbo's hand, that kept Bilbo from slaying Gollum when he'd had the chance. Gollum was much like a hopeless drug addict, and as terrible as such a person in that condition is, the response is to try everything to help the addict, even when there seems no hope left. Frodo also understands Godly wisdom here, again from Gandalf's earlier words (I'm paraphrasing here). Many a man deserves death, but are you the one to deal it? Many a man deserves life but receives death -- can you give it to him? Here Frodo shows that he will not be the one to execute God's wrath and punishment, the Christian concept that "Revenge is mine, saith the Lord" and God alone has the power over life and death. Frodo also will not be consumed with hate, anger or revenge. Consider the similar Biblical examples, such as when David hid from King Saul. Even when David has the chance to kill Saul, who has been actively hunting and trying to kill David, David will not act in like manner -- he spares Saul's life -- but allows that this matter is for God alone to handle.