Did Tolkein ever explain, in the books or his letters, why so much power was put into physical objects, rings? And what power did those rings actually hold, anyway? Status symbol?

Did Tolkein ever explain, in the books or his letters, why so much power was put into physical objects, rings?

That's straight from the Norse myths he drew from. See: Ring Cycle by Wagner.

Well, yes, but I meant contextually.

IIRC, both Galadriel and Elrond were able to use their rings to preserve the "refuge" status of Lothlorien and Rivendell, respectively. Lothlorien was much more secretive and also had that funky time-stands-still thing going on through the power of her ring, and Rivendell also managed to remain hidden from prying eyes due to Elrond's ring. As for Gandalf's, isn't it implied that he used the power of his ring to keep the fires of fighting against Sauron alive? "I am the wielder of the flame of Anor. The dark fire will not avail you, flame of Udun!"

Gandalf's ring was associated with fire, Galadriel's with water. What was Elrond's?

Elrond's was air, I believe.

ETA: No Earth ring, that means. Hmm.

Gandalf's ring was associated with fire, Galadriel's with water. What was Elrond's?

Gandalf's and Galadriel's ring powers show in various symbols also: Gandalf's fireworks, and use of fiery magicks on Weathertop (and flaming pinecones, although Tolkein didn't know about his ring then); Galadriel's water-fountain-mirror, and the gift-giving of boats on the river.

What about the Dwarven rings, or the rings of Men? Not to pelt you with questions--I'm just very curious.

I don't think any of the other Rings were formally element-associated. The dwarven rings were supposed to be good with gold, supposedly.

I think the Dwarf and Man rings were substantially lesser than the Elf rings -- they were, like, pawned off on assistants to make, whereas Celebrimbor made the Elf rings himself. This is why the Elf rings are more powerful, and have names, and not-coincidentally have not led their owners weeping and screaming to Sauron's doorstep, as the other sets of rings have done.

Certainly, in the text, the One Ring changes the user's perception, in addition to making him invisible. It also changes how the user feels about himself -- Samwise the Brave, Gollum the Great -- making him feel more powerful in quasi-benevolent or fishy ways, depending on his own nature. Sam scares the daylights out of the Cirith Unglo people, basically by dint of having the ring (whether or not it's on at any given moment); they see him as something far more powerful than he actually is in physical form.

People tend to flock towards the Ring, or its bearer: several times, when critters attack the Fellowship, they go for Frodo first.

Sauron made the dwarf and man rings specifically to enthrall the users, I think.