To say definitively if the One Ring is or is not sentient may not in the end be possible. To do so would surely require an attentive and thorough examination of the question. I tend to believe that it is not, but I also think that the ambiguity is both intentional and important. I am not pursuing that overall question here today, only a portion of it that has only recently become clear to me.
It struck me that Of Aulë and Yavanna supplies important testimony against the sentience of the Ring. Here's the passage in question (emphases mine):
Now Ilúvatar knew what was done, and in the very hour that Aulë's work was complete, and he was pleased, and began to instruct the Dwarves in the speech that he had devised for them, Ilúvatar spoke to him; and Aulë heard his voice and was silent. And the voice of Ilúvatar said to him: 'Why hast thou done this? Why dost thou attempt a thing which thou knowest is beyond thy power and thy authority? For thou hast from me as a gift thy own being only, and no more; and therefore the creatures of thy hand and mind can live only by that being, moving when thou thinkest to move them, and if thy thought be elsewhere, standing idle. Is that thy desire?'
Then Aulë answered: 'I did not desire such lordship. I desired things other than I am, to love and to teach them, so that they too might perceive the beauty of Eä, which thou hast caused to be. For it seemed to me that there is great room in Arda for many things that might rejoice in it, yet it is for the most part empty still, and dumb. And in my impatience I have fallen into folly. Yet the making of things is in my heart from my own making by thee; and the child of little understanding that makes a play of the deeds of his father may do so without thought of mockery, but because he is the son of his father. But what shall I do now, so that thou be not angry with me for ever? As a child to his father, I offer to thee these things, the work of the hands which thou hast made. Do with them what thou wilt. But should I not rather destroy the work of my presumption?'
Then Aulë took up a great hammer to smite the Dwarves; and he wept. But Ilúvatar had compassion upon Aulë and his desire, because of his humility; and the Dwarves shrank from the hammer and were afraid, and they bowed down their heads and begged for mercy. And the voice of Ilúvatar said to Aulë: 'Thy offer I accepted even as it was made. Dost thou not see that these things have now a life of their own, and speak with their own voices? Else they would not have flinched from thy blow, nor from any command of thy will.' Then Aulë cast down his hammer and was glad, and he gave thanks to Ilúvatar, saying: 'May Eru bless my work and amend it!'
(S 43-44)
Without the direct intervention of Ilúvatar, all of Aulë's power and craft and love cannot give sentience or consciousness to the Dwarves. Now Of Aulë and Yayanna dates from 1958, so we must naturally take care when using it to support a point about The Lord of the Rings. Yet the notion of making something in mockery recalls the remarks of Treebeard at TT 3.iv.486 and of Frodo at TT 6.i.914: 'The Shadow that bred them can only mock, it cannot make: not real new things of its own. I don't think it gave life to the orcs, it only ruined them and twisted them....' So, it seems clear enough that, when writing The Lord of the Rings, Tolkien already had in mind some version of the principle we see several years later in Of Aulë and Yayanna.
The story that Aulë made the Dwarves arose first in the 1930s, but Ilúvatar plays no role in it and the Dwarves have 'no spirit indwelling, as have the Children of Ilúvatar' (Lost Road, 129), though here this does not deprive them of sentience. This strongly suggests that Tolkien's thought was already moving along the lines we see later, even if he had not yet decided that only Ilúvatar could create autonomous beings which have 'a life of their own, and speak with their own voices'. In letter 153, moreover, written only weeks after the publication of The Fellowship of the Ring in 1954, Tolkien points out that while Melkor could have made the flesh and blood of the orcs by the power that was in him, he could not have given them souls or spirits, because that is not a power Ilúvatar 'delegated'. In the same letter he also remarks: 'when you make Trolls speak you are giving them a power, which in our world (probably) connotes the possession of a 'soul'. (Compare also the implicit link between consciousness and speech in Treebeard's remark that the old Elves woke the trees up and taught them to speak [TT 3.iv.468]). What Melkor could not do, Aulë and Sauron could not have done either.
Note, too, that Gandalf says Sauron 'let a great part of his former power pass into [the Ring], so that he could rule all the others' (FR 1.ii.51), and that, if the Ring is destroyed, Sauron 'will lose the best part of the strength that was native to him in the beginning', which would reduce him to 'a mere spirit of malice that gnaws itself in the shadows, but cannot grow again or take shape' (RK 5.ix.878). Here we see a clear distinction drawn between Sauron's spirit and his power or strength. The Ring contained his power, but not his spirit. Nor could he give it one. So whatever sentience or consciousness the Ring may possess, if it should possess any at all, seems little likely to have arisen from Sauron's having endowed it with his power (which he did) or with his spirit (which he did not do). It was, however, 'fraught with his malice' according to Elrond (FR 2.ii.254), that is, 'furnished with' or 'filled with', 'carrying with it as an attribute', 'destined to produce' (OED). Which is not to say that it feels malice.
What we have seen here argues against the sentience of the Ring. There are other passages that bear on this question in different ways, and other objects that may or may not be sentient, but they are not my concern here. I shall return to them in time.