During the journey to Gondor in The Lord of the Rings, the Riders of Rohan meet with a group of hunter-gatherers called the Druedain - Tolkien gives more information on the subject in notes published posthumously by his son Christopher in Forgotten Tales
These are simple, ugly, short-lived, and illiterate Men - who have various kinds of natural magical abilities - for example, they can make statues of themselves (which the Riders call Pukel-men) which can be infused with abilities such as to be vigilant and defend their territory against enemies. Another magical personage who lives in Original Participation is Tom Bombadil.
Then there are the High Elves - such as Galadriel or Glorfindel, who are highly intelligent ('wise'), beautiful, 'immortal' (immune to illness, able to live for the duration of the earth's life, unless slain), and the inventors of language and writing. The High Elves are also magic, able to make food, drink, clothing and ropes with extraordinary properties; see true visions in water; also ring, jewels and weapons with remarkable properties. This High magic is not a matter of trance-like sympathetic identification - but is purposive and fully conscious process.
The other races are arrayed in between these magical extremes in a way which corresponds exactly to Owen Barfield's description of the evolution of human consciousness - from the first magical stage of Original Participation in which human consciousness blends with its surroundings; through a middle and non-magical stage in which consciousness is detached from the world, and
Hobbits and most Men (and, I would say, Ents) are of the completely non-magical stage in the evolution of consciousness except insofar as they become 'elven' - for example Frodo becomes somewhat magical after being formally made an Elf Friend by the High Elf, Gildor. Frodo's is therefore an example of the early stage of Final Participation.
Dwarves are slightly magical - mainly in their technology - for example the Arkenstone (in The Hobbit)
is clearly a magical jewel along the lines of the Silmaril). My feeling
is that this is a developed, intelligent and wise ability of only the
most 'evolved' dwarves - and therefore a partial Final Participation.
The Numenorean Men are also magical - and this is again the elven magic of Final Participation - partly because of the lineage of HIgh Elven (and Maia - angelic) ancestry, and partly from a blessing by the Valar at the time of their dwelling in Numenor. We see this only in Aragorn and Denethor - for example their ability to control the Palantir, and the healing powers of Aragorn which can (uniquely) combat the dark magic of the Witch King Nazgul.
If we were to fuse Tolkien and Barfield (something which did not happen in 'real life') we would regard the elven strain in the Numenoreans and in Frodo as the first inklings of a return to a magical relationship with 'the world' which had been known to the Druedain - but at a higher, purposive and fully-alert way.
The terrible history of Numenor, and the sad fates of Denethor and (to a lesser extent) Frodo also show the perils of this future - in a pessemistic fashion very characteristic of Tolkien's Weltanschauung. Barfield, by contrast, saw this future as Man's destiny: desirable and in a sense necessary - but not inevitable.