The Horn of Boromir:

A horn carried by the eldest son of the Stewards of Gondor. Boromir, son of Denethor was its last carrier. It was cloven in two at his death by orcs.
Then maybe you can see it it in your mind's eye: a great horn of the wild ox of the East, bound with silver, and written with ancient characters. That horn the eldest son of our house has borne for many generations; and it is said that if it be blown at need anywhere within the bounds of Gondor, as the realm was of old, its voice will not pass unheeded. (LOTR.692)

The Horn of the Mark:

The horn given to Meriadoc Brandybuck, by Éowyn at their parting.
Then Éowyn gave to Merry and ancient horn, small but cunningly wrought all of fair silver with a baldric of green; and wrights had engraven upon it swift horsemen riding in a line that wound about it from the tip to the mouth; and there were set runes of great virtue. (LOTR.1014)

It was with this horn that Merry summoned the hobbits during the Battle of Bywater.

Herugrim:

Théoden's sword.

Helm of Hador:

Another name for the Dragon Helm of Dor-lómin.

Herblore of the Shire:

The book written by Meriadoc Brandybuck, about the plants in the Shire. Unfortunately the only surviving parts of the book are sparse and only concern Pipe-weed. The fragments have been included in the text of the Red Book.

The Hobbit
The Lord of the Rings
The Silmarillion
The Complete Guide to Middle-Earth by Robert Foster
The Unfinished Tales