Game of Thrones/Lord of the Rings villain swap (warning- major spoilers for season seven of GoT).

[Elheru Aran]

I dunno, I wouldn't be that confident about the Valar and/or Eru intervening directly on Middle-Earth. The last time Eru intervened was because Numenor was starting to become a threat to the Valar, and his solution was to separate Valinor from Arda permanently. This IIRC was after Mandos asked him directly to do something. The Maiar did come to Middle-Earth after that point, but Gandalf and Saruman are the only two really doing anything as far as we know (forget Radagast) and even that is mostly along the lines of encouragement and a little magic when it comes to Gandalf. Saruman has to build up an entire army to do anything rather than just snapping his fingers and making things so. I suspect the Valar likewise might be less powerful than they tend to be given credit for.

[The Romulan Republic]

And as always in a LOTR scenario we have to take into account the Valar (and possibly Eru). While the Valar had laid down their official guardianship of Middle Earth they still sent the Istari over to Middle-Earth to help challenge Sauron. Clearly they felt that they hold some degree of responsibility, even if they did not fight Sauron directly. White walkers suddenly appearing out of nowhere and trashing Minas Tirith while Sauron regains the Ring, possibly gains control of the White Walkers and launches his own slaughter campaign is the kind of the thing which could provoke the Valar into taking some form of direct action. I don't see the White Walkers and Sauron posing much of a challenge to the Valar if it came down to it.

Eru of course could wipe them all out in an instant though I assume that since the White Walkers didn't get destroyed the moment they entered Middle-Earth he allowed the swap to take place.

Well, the films don't really discuss the Valar at all, except (I think) name-dropping them in passing.

But if we assume that their role is the same as in the books unless explicitly contradicted...

Well, I'm pretty sure they won't intervene directly, unless we simply toss out Tolkien's whole mythology. Maybe an extra-dimensional invasion would change that. There's really no way to know, I suppose.

[NecronLord]

I dunno, I wouldn't be that confident about the Valar and/or Eru intervening directly on Middle-Earth. The last time Eru intervened was because Numenor was starting to become a threat to the Valar, and his solution was to separate Valinor from Arda permanently. This IIRC was after Mandos asked him directly to do something. The Maiar did come to Middle-Earth after that point, but Gandalf and Saruman are the only two really doing anything as far as we know (forget Radagast) and even that is mostly along the lines of encouragement and a little magic when it comes to Gandalf. Saruman has to build up an entire army to do anything rather than just snapping his fingers and making things so. I suspect the Valar likewise might be less powerful than they tend to be given credit for.

You're forgetting an instance.

Tolkien's explicit that this was the intervention of Illuvatar directly that restored Gandalf, not the Valar.

Gandalf really 'died', and was changed: for that seems to me the only real cheating, to represent anything that can be called 'death' as making no difference... He was sent by a mere prudent plan of the angelic Valar or govenors; but Authority had taken up this plan and enlarged it, at the moment of its failure. 'Naked I was sent back- for a brief time, until my task is done'. Sent back by whom, and whence? Not by the 'gods' whose business is only with this embodied world and its time; for he passed 'out of thought and time'. Naked is alas! unclear. It was meant just literally, 'unclothed like a child' (not disincarnate), and so ready to receive the white robes of the highest. Galadriel's power is not divine, and his healing in Lorien is meant to be no more than physical healing and refreshment."

We generally suspend such things for vs. debates though, as it would produce the perverse result that LotR is unbeatable, what with having an all-powerful god in the good guys' corner.

[The Romulan Republic]

Well, then, it becomes not a question of weather the White Walkers and Sauron will lose, but simply of how Illuvatar will bring about their defeat, yeah.

[Tribble]

I dunno, I wouldn't be that confident about the Valar and/or Eru intervening directly on Middle-Earth. The last time Eru intervened was because Numenor was starting to become a threat to the Valar, and his solution was to separate Valinor from Arda permanently. This IIRC was after Mandos asked him directly to do something. The Maiar did come to Middle-Earth after that point, but Gandalf and Saruman are the only two really doing anything as far as we know (forget Radagast) and even that is mostly along the lines of encouragement and a little magic when it comes to Gandalf. Saruman has to build up an entire army to do anything rather than just snapping his fingers and making things so. I suspect the Valar likewise might be less powerful than they tend to be given credit for.

The Valar intervene when all hope has been lost and the alterative is letting evil run rampant forever over Middle-Earth. They fought with Melkor when he first arrived and claimed Arda, they fought him again when they realised the elves had woken and that Melkor was trying to corrupt him, and they fought him (as the much weaker Morgoth) a third time at the end of the First Age during the War of Wraith, when it was clear that he was on the verge of total victory. IMO they probably would have fought Morgoth much sooner were it not for Noldor's rebellion, Feanor's Oath and the Kinslaying... that kind of tied their hands for awhile.

However, even at the height of his powers in the Second Age Sauron never reached the point where all resistance was broken, so there was direneed for them to directly intervene. In the Third Age the resistance was much weaker but the good guys could still win with some help which is why they sent the Istari. Had that failed I really don't think they would have let Sauron sit there and dominate Middle-Earth forever.

Regarding Numenor, I always saw that as a jurisdictional issue - IMO they had more than enough power to defeat the invasion fleet (particularly since Manwe and Ulmo command the oceans and the winds) but they didn't feel they had the right to. Even corrupted Men were still children of Iluvater, and a big part Men's gift was specifically allowing them the ability to shape their own destiny beyond that of the Music of the Ainur. Men weren't really a part of the general Music so to speak so the Valar didn't know what to do.

As for the Valar's power... wars involving the Valar tend to wreck continents. Which is probably why they usually stay back since they would want to avoid collateral damage where possible. No way Sauron and the White Walkers survive if they decided to go all out.

We generally suspend such things for vs. debates though, as it would produce the perverse result that LotR is unbeatable, what with having an all-powerful god in the good guys' corner.

Well ya, LOTR does have an all-powerful God who is also on the good guys side, so technically they are pretty much unbeatable in their universe should he decide to get involved. That being said Eru is usually pretty hands-off most of the time, so I guess we can assume that he decided to let things play out, or that it was part his plan the whole time etc.

Gandalf is kind of an odd case... IIRC Maiar can't be killed, as their spirit stays in Arda even if their physical form is destroyed. Elves' spirts also stay on Arda, and there are cases where some were resurrected (such as Glorfindel after defeating a Balrog). Only Men's spirits were known to leave Arda entirely as that was part of their Gift. Maybe Eru intercepted Gandalf's spirit or something? Morgoth was beheaded and his spirit trapped in some kind of limbo, while Sauron's and Saruman's spirits were shown to physically manifest themselves before being blown away / scattered by the Valar.