- Creation of the Universe and the Valar:
Ilúvatar gave to their vision Being, and set it amid the Void, and the Secret Fire was sent to burn at the heart of the World; and it was called Eä.
- Creation of the Children of Iluvatar (Men and Elves):
as this vision of the World was played before them, the Ainur saw that it contained things which they had not thought. And they saw with amazement the coming of the Children of Ilúvatar, and the habitation that was prepared for them; and they perceived that they themselves in the labour of their music had been busy with the preparation of this dwelling, and yet knew not that it had any purpose beyond its own beauty. For the Children of Ilúvatar were conceived by him alone
the Valar, having had no part in the devising of the Children of Eru, do not know fully the purposes of Eru concerning them, nor the final ends that he prepares for them.
Ilúvatar spoke again and said: '...when the time comes I will awaken them, and they shall be to thee as children; and often strife shall arise between thine and mine, the children of my adoption and the children of my choice.'
- Defeat and banishment of Melkor:
not until the last, and not then except by the express command of Eru and by His power, was Melkor thrown utterly down and deprived for ever of all power to do or to undo.
Ilúvatar showed forth his power, and he changed the fashion of the world; and a great chasm opened in the sea between Númenor and the Deathless Lands, and the waters flowed down into it, and the noise and smoke of the cataracts went up to heaven, and the world was shaken. And all the fleets of the Númenóreans were drawn down into the abyss, and they were drowned and swallowed up for ever.
He was sent
by a mere prudent plan of the angelic Valar or governors; 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 ofthought and time'.
- The ultimate destruction of the Ring (thanks to ALS):
Frodo deserved all honour because he spent every drop of his power of will and body, and that
was just sufficient to bring him to the destined point, and no further. Few others, possibly no others
of his time, would have got so far. The Other Power then took over: the Writer of the Story (by
which I do not mean myself), 'that one ever-present Person who is never absent and never named'
(as one critic has said).
All quotes from the Silmarillion, save the last two which were from Letters #156 and #192.
Note: However as implied in the last quote, Eru is ever-present, so there may be instances where he directly interfered (and likely there were) other than those listed above, but we would not know it and are not told it.