Rings, like all jewelry, are indeed very significant in much of the Old English literature. Gift giving stools were common in the halls where the clans (towns) would meet and eat and/or sleep if the persons did not own their own accomodations. The leader of the clan, the gift giver, would bestow jewelry on someone who embodied great qualities. This was generally conducted after a battle, or some heroic feat. The recipient would wear the jewelry proudly as a sign that he was favored by the ruler. Rings, were generally not given at the gift giving stool. Beowulf is a really good example of this. The Wanderer is an example of one who has been cast away from his clan and has lost his status - no home, no king, no jewelry.

The more jewelry one possessed, the more favored they were. In addition, rings symbolized eternity, no beginning and no end in their circular nature. Those who were thanes (rulers of their clans) generally used the ring they wore to carry the insignia of their position. In times when most people could not read or write, including the rulers, the ring was used to 'seal' contracts or decrees drawn up by counselors or scribes (who could write).

So the rings in FOTR are indeed tied to historic and mythological tales. In the dark ages, there was no differentiation between myth and truth- it was all about what made a good story. And as most people knew the history through the oral tradition, they did not concern themselves that people thousands of years later would not be able to sort out which is which. :)

My favorite concept regarding the rings given to the men is in their number. In Anglo Saxon myth, 9 is the perfect number. It is the last of the single digit numbers and used consistently in Ango-Saxon literature for symbolism of strength and magic.

Examples:
When Odin sacrificed himself to himself, he hung upon the gallows for nine days and nine nights. In return, he learned eighteen (twice nine) charms (or runes).
There are nine worlds that are supported by Yggdrasil.
Every ninth year, people from all over Sweden assembled at the Temple at Uppsala to sacrifice slaves & animals.
The god-guardian of the Bifrost Bridge, Heimdall is said to have been the son of nine mothers, possibly the nine daughter of Aegir identified as the waves of the sea.
In the Skirnismal Freyr is obliged to wait nine nights to consummate his union with Gerd.
In the Svipdagsmál, the witch Groa grants nine charms to her son Svipdag.
In Fjolsvinnsmal Laegarn's chest is fastened up with nine locks.
In the Ragnarok Thor kills Jormungand but staggers back nine steps before falling dead himself, poisoned by the venom that the snake spewed over him.
According to the very late Trollkyrka poem, the fire for the blót was lit with nine kinds of wood.
There are Nine Valkyries.

It is no coincidence that there are 9 members of the fellowship. It has been a few years since I read the Sim. but I seem to recollect quite a few nines in there as well.

Okay, you can wake up now, I am finished droning.