The Star of Earendil (headgear): A headband with a glowing gem set in it, made in likeness of the silmaril that Earendil wore, and imbued with some of its light. +2 light, activates to do some kind of sun paladin thing (I haven't played them enough to remember their abilities), maybe something else? Basically an alternative to the Helm of Hammerhand.
The mummified egg-sac of Ungoliant (not wearable): By what strange fate this survived, you cannot imagine. Dry and dusty to the touch, it still seems to retain some of its foul mother's (*) unending hunger. -1 light, activate to summon friendly spiders.
(*) The word "mother" seems wrong when talking about a spider's egg. "parent"? "sire" is obviously wrong, "dam" seems too obscure.. any ideas?
The balrog's wings (cloak -- or necklace, if we don't have cloaks): A great cape of shadow, its wings stretching out to either side. +10 invisibility _if_ not wielding a light source. +20% fire resistance. If wielding a light source, -1 light and creatures randomly flee in terror.
Sting (well, why not?) -- extra damage against orcs, extra damage against spiders, immune to spider webs.
The Palantir of Minas Tirith (not wearable): Used by Denethor in his wisdom, and then misued by Denethor in his folly. It is said that if any but the strongest of will look into its depths, they will see nothing but two burning, withered hands. Activate for magic mapping, but only if willpower > 30.
The Palantir of Minas Ithil (not wearable): Abandoned by Gondor during its long decline, this was captured by the Nazgul and delivered to Sauron before the War of the Ring. Sauron used to great effect, not least in keeping watch on his many rebellious servants. Activate to detect servants of Sauron (i.e. orcs and trolls).
[I'm assuming the king of Gondor keeps the Orthanc stone
The collar of Huan (necklace): This collar was once worn by Huan, the Hound of Valinor. How it escaped the ruin of Beleriand, you will never know. All canines generated friendly, activate to summon friendly dogs.