[Legolas]

Forgive the long quotes, but this was something Tolkien obviously thought to be very important and made it central to the progression of Man's kingdoms.

However it is interesting that no-one in Middle Earth actually appears to worship Eru, ask him to intercede on their behalf or even to mention him.

It is not so - both Men and Elves worshipped him (and dwarves, possibly).

Númenór is not 'Middle-earth' exactly, but it was no less a part of Arda. The Men of Númenór acknowledged and praised Eru upon the Pillar of Heaven...

The Silmarillion(*)

But in the midst of the land was a mountain tall and steep, and it was named the Meneltarma, the Pillar of Heaven, and upon it was a high place that was hallowed to Eru Ilúvatar, and it was open and unroofed, and no other temple or fane was there in the land of the Númenóreans.

Letter No. 156

The Númenóreans thus began a great new good, and as monotheists; but like the Jews (only more so) with only one physical centre of 'worship': the summit of the mountain Meneltarma 'Pillar of Heaven' – literally, for they did not conceive of the sky as a divine residence – in the centre of Númenor; but it had no building and no temple, as all such things had evil associations.

And the Downfall of Númenór essentially starts in the days of Tar-Ciryatan and his son as the Númenóreans clash with Manwë in wanting to go to Valinor and such. This leads directly to perhaps the most important factor - the divide among the Númenóreans and the cessation of praise for Eru upon the Pillar of Heaven.

But those that lived turned the more eagerly to pleasure and revelry, desiring ever more goods and more riches; and after the days of Tar-Ancalimon the offering of the first fruits to Eru was neglected, and men went seldom any more to the Hallow upon the heights of Meneltarma in the midst of the land.*

The Eldar, too, acknowledged and praised Eru as their sole creator and God.

In The Lord of the Rings the conflict is not basically about 'freedom', though that is naturally involved. It is about God, and His sole right to divine honour. [b]The Eldar and the Númenóreans believed in The One, the true God, and held worship of any other person an abomination[b]. Sauron desired to be a God-King, and was held to be this by his servants; if he had been victorious he would have demanded divine honour from all rational creatures and absolute temporal power over the whole world. (183)

The Elves also had their fall (at least the Noldorin Exiles) in denying Eru praise, for they left it behind in Aman, holding contempt for those who stayed there, along with their practices:

The High Elves were exiles from the Blessed Realm of the Gods (after their own particular Elvish fall) and they had no 'religion' (or religious practices, rather) for those had been in the hands of the gods, praising and adoring Eru 'the One', Ilúvatar the Father of All on the Mt. of Aman. (156)

Dwarves would've praised Eru also, at least in their beginnings:

...for Aulë had done this thing not out of evil desire to have slaves and subjects of his own, but out of impatient love, desiring children to talk to and teach, sharing with them the praise of Ilúvatar and his great love of the materials of which the world is made. (212)

This quote notes the progression of such worship to 'present' in the Middle-earth mindset. This letter goes into a discussion of Númenórean religion, but unfortunately, CT (or the other editor, Humphrey Carpenter) chose to cut the letter off after this statement.

We are in a time when the One God, Eru, is known to exist by the wise, but is not approachable save by or through the Valar, though He is still remembered in (unspoken) prayer by those of Númenórean descent. (297)

A further explanation comes of this progression later on:

Men have 'fallen' – any legends put in the form of supposed ancient history of this actual world of ours must accept that – but the peoples of the West, the good side are Re-formed. That is they are the descendants of Men that tried to repent and fled Westward from the domination of the Prime Dark Lord, and his false worship, and by contrast with the Elves renewed (and enlarged) their knowledge of the truth and the nature of the World. They thus escaped from 'religion' in a pagan sense, into a pure monotheist world, in which all things and beings and powers that might seem worshipful were not to be worshipped, not even the gods (the Valar), being only creatures of the One. And He was immensely remote. (156)

How did they fall? The treasures of the world won their attention, and the (envy of the) immortality/majesty of Valinor and the Elves won their hearts and mind. Even in the Faithful, those that did not push for war on Valinor, Elendil, his sons, and his men failed to reestablish worship of Eru, though they retained other Númenórean values:

the Faithful in Númenor, who had refused to take pan in the rebellion, [...] established a kind of diminished memory of Númenor in Exile on the coasts of Middle-earth – inheriting the hatred of Sauron, the friendship of the Elves, the knowledge of the True God, and (less happily) the yearning for longevity, and the habit of embalming and the building of splendid tombs – their only 'hallows': or almost so. But the 'hallow' of God and the Mountain had perished, and there was no real substitute. Also when the 'Kings' came to an end there was no equivalent to a 'priesthood': the two being identical in Númenórean ideas. So while God (Eru) was a datum of good Númenórean philosophy, and a prime fact in their conception of history. He had at the time of the War of the Ring no worship and no hallowed place. And that kind of negative truth was characteristic of the West, and all the area under Numenorean influence: the refusal to worship any 'creature', and above all no 'dark lord' or satanic demon, Sauron, or any other, was almost as far as they got. They had (I imagine) no petitionary prayers to God; but preserved the vestige of thanksgiving. [...] It later appears that there had been a 'hallow' on Mindolluin, only approachable by the King, where he had anciently offered thanks and praise on behalf of his people; but it had been forgotten. ... (156, continued below)

As Tolkien said often, the mixing of Man and Elf (in Dior and Earendil) served as part of the idea in Men eventually taking the Elves' place as rulers of the land ("The entering into Men of the Elven-strain is indeed represented as part of a Divine Plan for the ennoblement of the Human Race, from the beginning destined to replace the Elves") - this meant in terms of love for God too, which many could easily overlook. Aragorn would be the one to turn Gondor in the right direction again (as the Númenórean influence was excavated):

... It was re-entered by Aragorn, and there he found a sapling of the White Tree, and replanted it in the Court of the Fountain. It is to be presumed that with the reemergence of the lineal priest kings (of whom Lúthien the Blessed Elf-maiden was a foremother) the worship of God would be renewed, and His Name (or title) be again more often heard. But there would be no temple of the True God while Númenórean influence lasted. (156)

So why do we hear calls of Elbereth and petitions to the Valar (from Frodo, Gildor's party's song, Legolas, Sam, Damrod, etc.) instead of Eru? A note in paranethesis from the previously quoted letter explains...

Those under special Elvish influence might call on the angelic powers for help in immediate peril or fear of evil enemies. (footnote: The Elves often called on Varda-Elbereth, the Queen of the Blessed Realm, their especial friend, and so does Frodo.) (156)

The Elves still acknowledged the majesty and authority of the Valar; further, they recognized (were aware) that the Valar were in more of a position to help them - physically present in Arda - while the One is remote, subtle, and does not directly intervene often. It's just as one might call out to a guardian angel.

Olorin_TLA said

Basically, if a mortal were to act like Eru, we'd hope Saruon ate them.

This is not exactly the case; rather, it is presented in a misleading manner. If one were to act like Eru in terms of thinking they could create, dominate, etc., we would wish them to stop, but this is simply because a mortal *cannot* be Eru, nor if the mortal even had said power, could they exercise it in the gracious manner that Eru does. This is precisely why Morgoth and Sauron are hated, cause so much suffering, and ultimately fail.

Bethberry said

an angel, sent to block or obstruct human activity in such a way as to teach people something about their own weaknesses and foibles.

In 'sent to...', do you mean to imply that Satan was sent intentionally by God to do so?

As for the chessboard analogy, I do not think it works. If Middle-earth was a chessboard, there would be a number of different parties, but if you still reduced it to two sides - good and evil - each piece would be able to move itself. In that point of view, Eru is just as he is presented in the text - the Creator. He would've made the board and each piece, and place the restrictions on their movements (the parallel being the limitations of power); He would not be the one moving the pieces. Each piece has a will of its own.