Is there something I can do with the rings/amulets I'm not using?

There are a few vendor recipes about trinkets such as rings and amulets here.

And here is a list of everything that has to do with rings and amulets, taken from mentioned link.

Full rare sets

These recipes require a full set of rare items. A full set is capable of filling all item slots in the inventory screen (not including flasks or the alternate weapon set). Specifically, it consists of:

• One of the following:
  • Two-Handed Weapon ×1
  • One-Handed Weapon ×1 and Shield ×1
  • One-Handed Weapon ×2
• Helmet ×1
• Body Armour ×1
• Gloves ×1
• Boots ×1
• Belt ×1
• Amulet ×1
• Ring ×2

  Reward/Level of lowest-level item
  1 Orb of Chance/1 to 59
  2 Orbs of Chance/1 to 59, all unidentified OR all 20% quality
  3 Orbs of Chance/1 to 59, all unidentified AND all 20% quality
  1 Chaos Orb/60 to 74
  2 Chaos Orbs/60 to 74, all unidentified OR all 20% quality
  3 Chaos Orbs/60 to 74, all unidentified AND all 20% quality
  1 Regal Orb/75 to 100
  2 Regal Orbs/75 to 100, all unidentified OR all 20% quality
  3 Regal Orbs/75 to 100, all unidentified AND all 20% quality

Vendor recipes involving rings & amulets

Unless otherwise stated, the item level and rarity of the item produced are both equal to the lowest item level and rarity among all items required for the recipe.

  1 Iron ring + 1 Red skill gem = 1 Ruby ring (white)
  1 Iron ring + 1 Green skill gem = 1 Topaz ring (white)
  1 Iron ring + 1 Blue skill gem = 1 Sapphire ring (white)
  1 Two-stone ring of each combo (3 total) = 1 Prismatic ring (white)
  7 Iron rings + 1 Coral ring (rare) = 1 Coral amulet (rare)
  7 Iron rings + 1 Paua ring (rare) = 1 Paua amulet (rare)
  1 Amulet (any) + 3 skill gems (1 of each color) = 1 onyx amulet
  1 Amber amulet + 1 Lapis amulet + 1 Orb of Transmutation = 1 Agate amulet
  1 Jade amulet + 1 Lapis amulet + 1 Orb of Transmutation = 1 Turquoise amulet
  1 Amber amulet + 1 Jade amulet + 1 Orb of Transmutation = 1 Citrine amulet
  5 magic items of same type = 1 new magic item of same type (*Item level of resulting item equals lowest item level among components*)

Crafting!

The following vendor recipes add or remove modifiers on items

Ring or Amulet + Orb of Augmentation + Amnethyst flask = Ring or amulet with +x% Chaos Resist
Magic Wand x1 + Ruby/Sapphire/Topaz ring + Orb of Alteration = Wand with +1 to level of Lightning/Fire/Cold (depending on resist of ring used in crafting) Gems in this item x1

Changing bandit rewards

It is possible to change your Bandit choice. To do this, execute one of the following Vendor Recipes on the preferred Difficulty.

20 Orbs of Regret + 1 Amber Amulet = Book of Reform (Oak)
20 Orbs of Regret + 1 Jade Amulet = Book of Reform (Kraitlyn)
20 Orbs of Regret + 1 Lapis Amulet = Book of Reform (Alira)
20 Orbs of Regret + 1 Onyx Amulet = Book of Reform (Eramir (skill point))

One notable example - if you have 60 unique rings, you can craft them into a Loreweave.