It seems as this is a much debated topic right now, and I'm not too sure my mind is made up either way, so I figured I'd post the opposite of the 'Rand not pulled from world of dreams' theory...
Lets look at a hypothetical situation...
Rand dies somehow. Not even going to attempt this question, but lets just say he does BEFORE Tarmon Gai'don. I think this would suck and wouldn't really bring the nations together, but lets pretend for a moment it happens.
By now, Logain has ousted Taim (or the cowardly lion has left already) and is the head of the Black Tower. Rand's gone, no Dragon Reborn to fight the last battle. Logain, being the noble hero guy he's been built up to be, leads the attack on Shayol Ghul, with Matt and Perrin leading all their prospective nations. Matt blows the horn, and lo and behold, here comes Rand with Hawkwing, eagle eye, etc. Rand is there to fight the last battle.
Some people think a hero goes into the horn as the last person they were, some think first. Some think it's just whatever you choose. I personally have not swung either way with them; there simply is not enough concrete proof to show either way, in my humble opinion. Therefore, I don't know whether he'll be Rand, Lews Therin, Guiare, George W., Mickey Mouse or Howard Stern while in T'A'R, But in this scenario, the Dragon will be at the last battle. This might explain some of our dreamers' dreams and our viewer's views.
Now, big problem with this: Can the heroes shed blood? I don't think they do. Did they in Falme? I'm not sure, but I'm leaning towards no. If they can't, Rand can't shed his blood on SG. Unless we're talking about blood family --Now that would answer that one, depending on how you interpret the prophecy. There are a lot of open ends to this; I'll be the first to admit it.
Anyway, I've tried thinking 'out of the box' with this one, hopefully inspiring a new and interesting theory. The likelihood of this happening is as good as any when RJ's in control, and we are not! Speculation, isn’t it great?
Until Nynaeve quits pulling that braid,
May you find water and shade! 
Raserei says: Ah! Nice creative thinking.
But you are right, if Rand is to literally to shed blood on the rocks of Shayol Ghul, then I don't think that can be fulfilled through this venue.
Perhaps the masses has something to say.
Comments
I just had a minor thought........
Rand is of the Aiel. They are his people, and the Aiel prophacy says that he will do away with a lot of them....
So I thought perhaps the Blood spilt<sp?> will be Rand's people ie the Aiel
Perhaps in a mass attempt at a rescue?
I have always been of the mind that Rand will die and be sent to Tel'aran'rhiod because Nynave was the one present when Moghedian ripped out Birgitte plus she's the healing guru. The fact that it is possible and we have learned so much about the knowlege one aquires while in the world of dreams leads me to think that this is a plaussible solution to dying and being reborn.
However, I have always thought that Logain's laughing over a paper-mache Rand, plus the Rand-as-begger fortellings would take place after the last battle when Logain, who has a much more regal bearing, would take over as head channeler all the time knowing that Rand is alive and well in retirement. They may even converse sometimes on matters but Rand will be done with the world and will slip into anonymity. In the fortelling Logain is stepping onto the black square that Taim has at the black tower so this would lead me to believe he will be head of male channelers. who knows.
As long as we're throwing out the "Dragon's Blood" theories... Isn't Galad Rand's blood?
I don't really see this as a possibility, but hey if we're mentioning the Aiel, why not?
I agree with the Logain and Rand the beggar after TG. I also think it would be a pretty cheap out for Rand to be ripped out.
Remember, Mat has already died and been reborn without having to go to any big extremes.
Anyways, back to Dragon Warrior VII (my main character is named Mat).
For some reason I have always tended towards the theory that Rand will be alive and well to fight the Last Battle. This makes sense with the blood on the rocks thing, as one of Min's viewings aroung Rand was black rocks wet with blood. This seems to mean that he will spill it, and therefore he has to be there in a corporeal sense.
But then again, I could be wrong.
(BTW, GEORGE W.????? WTH?)
Ruriha Sedai 
Aes Sedai of the Green Ajah
Officially On Holiday 
Middle-Earth Kiwi 
She Who Has Returned
Why does everyone assume that logain is going to follow after rand? Sure, he has a big following in the Black Tower, but Narishma is the one who'll follow after, and I can prove it.
Prophecy:"into the heart he thrusts the blade, ito the heart to hold their hearts, who pulls it out shall follow after, what hand can hold that dreadful blade."
Rand thrust callandor into the heart of the stone, and NARISHMA pulled it out on rand's orders. Most people will now be saying: but logain has 2 bonded sisters, and can use it safely. Well here's some news for ya...Narishma has already used it safely with 2 linked sisters. I believe that logain will be Narishma's sub-ordinate. Remember...before anyone had any clue that logain would ever be able to channel again, R.J. had already started telling us about Narishma, and how immensely powerful he would be. So HA!
Now to wait for people to point out the countless flaws that i was blind to. Hurray!
sincerely,
the lover of light and wisdom
the all-seeing eye
the wandering wotmaniac
I dont' think I ever said Logain would wield callandor. I happen to believe that it will be Narishma who'll continue to wield that. However, Logain WILL attain glory few can even dream of, according to Min, who we know is never wrong. Just thought I'd clear that up for you.
and that's jsut rude..."Ha!"
Welp, see ya later.
"Until Nynaeve quits yankin' that braid,
May you find water and shade."
I think that somewhere in book four or five one of the Aiel mentions that they will be almost destroyed at Shayol Ghul and they will be the "blood of the Dragon," but I'm not sure on this, and I'm not willing to go wading through . . .
I may be love's bitch, but at least I'm man enough to admit it. -- Spike
I'm pretty sure that Rand WILL die before the last battle, but I have always believed that Nynaeve will heal him. There has been hints that Nynaeve will not settle until she heals a corpse dead for three days... just a thought though...
(By the way, I'm a newbie here. Hello everybody!)
I do not see any imposabilities with this theory, only one minor change. Personally, since the DO is a god for all intents and purposes, I do not believe that he can possably be harmed by any living porson. However, as it is stated above and other theories and in the books, the heroes are not living people (with one notable exception). Rand will valiantly go to fight the last battle, get killed off (now thats what I call a dramatic chapter ending!), so there is the whole bolld on the rocks thing solved. Then things will go basicly as in the above theory with Mat blowing the horn and a now invincible Rand comming back with the rest on the heroes.
Telvin
..no
Since Rand is Lews Therin reborn, wouldn't he be in Tel'aran'rahoid as Lews Therin rather then Rand al'Thor?
unless he actually dies at shuol ghul, and is called back at the end of the battle by the horn
The theory about Rand coming back when the horn of valere is blown is a good theory, however that brings up a question? If and when Rand dies, Perrin and Mat will surely have the same fate, because the three Tavaren are tied together, thats why the DO doesn't care which one of the three dies. All the dark one has to do is kill one of the three and all three fail.
Warder to no one. 
need freedom to roll the dice!
need to be spammed!
Tel'aran'RAND...