Gollum

[Legate of Amon Lanc]

Originally Posted by hewhoarisesinmight

I'm sure hobbits couldn't turn into wraiths because of their inner strength

Well, the text implies that they could, but you are right that it surely isn't as easy as with "normal" Men. Because:

Originally Posted by LotR II, Chapter 1: Many Meetings

"They tried to pierce your heart with a Morgul-knife which remains in the wound. If they had succeeded, you would have become like they are, only weaker and under their command. You would have became a wraith under the dominion of the Dark Lord (...)

This text is referring to the Morgul-wound, of course, but I think the point is the same - the struggle was about Frodo's resistance, as it is said elsewhere, he could have faded rightaway:

Originally Posted by LotR II, Chapter 1: Many Meetings

And it seems that Hobbits fade very reluctantly. I have known strong warriors of the Big People who would quickly have been overcome by that splinter, which you bore for seventeen days.

The same goes for the Ring, I think, more or less. Fading, going into the wraith-world, et cetera. The Morgul-wound is just a quicker, easier way how to move a person to the wraith-world.

Originally Posted by LotR I, Chapter 2: Shadow of the Past

A mortal, Frodo, who keeps one of the Great Rings, does not die, but he does not grow or obtain more life, he merely continues, until at last every minute is a weariness. And if he often uses the Ring to make himself invisible, he [/I]fades[I]: he becomes in the end invisible permanently, and walks in the twilight under the eye of the dark power that rules the Rings. Yes, sooner or later – later, if he is strong or well-meaning to begin with, but neither strength nor good purpose will last – sooner or later the dark power will devour him.

Every mortal, including a hobbit could become a wraith. But it would take a great effort, and he would possibly have to wear it all the time (cf. below).

Originally Posted by Mansun

The fact that Gollum had a much increased lifespn also points to the likelihood of an undead wraith developing.

I think this is the other way around. If we analyze the quotation above, then we come to these conclusions:

1. The mortal who owns a Ring of Power does not die.
2. If he uses the Ring too often to become invisible, he "fades" (=becomes a Ringwraith).

So, it was not that Gollum's (or Bilbo's, as well) lifespan was increased because he started to become a wraith, but because he owned the Ring. And in addittion to this, when he used the ring too often, he would become a Ringwraith. These are two separate "abilities" of the Ring.

So, for Gollum (or Bilbo or Frodo), to "fade" (turn into a wraith) would need from them that they wear the Ring very often. The Men who later became Nazgul probably had them on most of the time, if not all the time - the Rings gave them power to command people, granted them wisdom, sorcerous powers or whatever, we can only guess. But Bilbo put the Ring on only when he wanted to disappear from the Sackville-Bagginses and in similar occasions; Frodo put the Ring on only few times and the main source of his "fading" was the Morgul-wound. Otherwise, he had no "physical" problems with the Ring, only psychical. And Gollum? Well, Gollum also didn't put it on in the later days:

For it was long since he had worn it much: in the black darkness it was seldom needed.

This is also why I think he was not near "fading" as well. And when he went out to search for it, he wanted it, yes, but he also was partially on his way to be cured from its influence. No knocking at the door of the wraith-world - during the journey with Frodo&Sam, Gollum was certainly going almost all right.

I divided Mansun's quite short question to three parts, because at the same time he puts it, answers it and says certain things which I'd like to look at separately. So:

Originally Posted by Mansun

If Gollum did not perish at Mount Doom, would it have been possible for him to return to his former self phsically or mentally?

I would say, he would have been "normal" himself, maybe lost, maybe desperate and crawling through the wilderness until dying from despair and weariness and all these old years falling on him. He would have completely free will, finally, so "mentally" he'd have the possibility to start anew. Whether he would or would not is an ethical and soteriological question, and that is for some other topic (and I think there are lots of these threads here at the Downs).
Speaking of "physically" - I don't think Gollum had actually changed "physically" (the same point about the slime). It is not that he mutated into an alien creature. For your question, I would answer no, of course he wouldn't look like a normal Stoor again. His change was given by living in the caves with no light (possibly big eyes capable to see in dark), living near the lake (arms&legs more capable of swimming), having very poor eating habits (very thin he had became), and the "slime" certainly meant nothing more or less than when Aragorn found him he was covered in slime because he was puddling in the mud and slimy water. As he did most of the time, so he was actually slimy all the time, but not from his own. Or maybe, his skin might have developed something like a "self-sliming system" to keep him wet, though... he probably wouldn't have need of something like this in the cave near the lake. But mainly, he did not become "something else" - he was still a Stoor, physically (if you took his DNA and scanned his skeleton and internal organs via X-rays, he would still be classified as Stoor).

Originally Posted by Mansun (continuing the previous)

Almost certainly not, as the Ring & he were like one, much like the Ringwraiths were with their rings. When the Ring was destroyed, Gollum would die

I see your point, but Gollum was not Sauron and not a Ringwraith. He was not one with the Ring. The only reason why I can imagine he might have died then is because the power that granted him so long lifespan would be destroyed. But we know that it didn't work like that: look at Bilbo, he also didn't die when the Ring was destroyed. This is the same - Gollum will maybe feel a lot older, but this is all. He might certainly live for some years more, not disappearing and leaving only empty clothes like the Nazgul did.

Originally Posted by Mansun (continuing the previous)

as the Ring has become his only reason for a will to live.

More psychically, I think. But you might have a point here (cf. what I said above, this question is for a much larger topic) - he didn't have anything else to hold to, any life ideal - like returning back home (he had none anymore) or opening a fish restaurant. When he lost his last reason to live, he might as well have jumped to the Orodruin himself (maybe attempting to save the Ring). But this is different from dying because the Ring was destroyed - there is nothing like the will of the Ring keeping him alive, no.

[Raynor]

Every mortal, including a hobbit could become a wraith.

I disagree (emphasis added):

Originally Posted by Of the rings of power and the Third Age, Silmarillion

The Dwarves indeed proved tough and hard to tame; they ill endure the domination of others, and the thoughts of their hearts are hard to fathom, nor can they be turned to shadows.

[Legate of Amon Lanc]

Oh, of course, I forgot the Dwarves... these were Men and Hobbits I had in mind. Dwarves... such a minority, who cares of them?

If the Ring has been destroyed, & Gollum didn't have the chance to jump into the fire to try & save it, he would most probably have lost consciousness & never regained it lol. The Ring made him merely continue, but once it is no more, he cannot continue as all the motivation & treacherous power of the Ring is taken away. He even said himself that once Ring died, he would die with it. Bilbo had not yet got to this stage of destruction, but if he was present to see it destroyed, he would see it as the end of a nightmare like Frodo.