If Frodo had thrown the Ring in right away

[Eruanna]

What would have happened to Gollum is certainly open to speculation. One thing for sure is that Frodo would, at least, still have all of his fingers

[mormegil]

I tend to agree that Gollum, if he survived, would be completely hopeless and miserable. His "addiction" as you called it would never be eased and would gnaw at him until he died. Now I think it's likely that he would have actually jumped into the fire as Eomer stated. However, had he not jumped into the fire he, like Sauron, may have been destroyed. His power and life was tied up in the ring and it's destruction could have brought about his own.

[Celebuial]

I agree partly with Mormegil, but I don't think Gollum or I suppose Smeagol (seeing as The Ring is gone), would've perished. Sauron, put some of his 'life force' into The Ring when it was created, thus binding his fate to that of The Ring. Gollum however, had 'an addiction' to The Ring, and although his fate was undoubtably tied up with the fate of The Ring in general, I find it hard to believe that he would be destroyed if The Ring was. Part of him, Gollum may have been destroyed, but I think it more likely that he would hang around to torment him until he died a long, long time later: Smeagol didn't willingly give all of himself up to The Ring; a small part of him resisted. Frodo, although he was in possession of The Ring for a much shorter time span, was permanently tormented by the thought of The Ring, even after its destruction. Maybe this suggests that Sauron's spirit was somehow reaching out to him from The Void, or maybe Eru never meant for such creatures to take such torment, and his mind was permanently scared. I don't think that part of Frodo was destroyed though, just that he saw the world differently, and had endured too much.

[eowyntje]

After they lost he ring, both Bilbo and Frodo aged quicker. Isn't it likely that Gollum, after having lived on the ring for over 500 years, would age very fast and die within a very short time after the distruction of the ring?
If of course he would not kill himself or be killed by the ring before such a thing could happen.

[Eomer of the Rohirrim]

Good idea; he might shrivel up and die within seconds, because he had the Ring for so long.

[obloquy]

I think it's possible that Gollum would've felt relieved. His actions and lust for the Ring might have been the Ring's will and not his own. Note that he calls the Ring "Precious" as well as the second voice that guides his more devious actions. Perhaps he would have been exhausted, as Frodo was, but maybe his seeming insanity and obsession would have been lifted with the Ring's destruction.

[Kitanna]

Supposing Frodo had willing thrown the Ring into the fires I think Gollum would have gone after Frodo. He probably would have fought with Frodo anyway. I honestly think he'd go in after it and drag Frodo down with him. After all Frodo was the one who destroyed his precious.