Dwarves are a race almost as popular as speakers of conlangs as are Elves.
Dwarves in mythology and folklore
Like the Elves, they originate in Germanic mythology, though similar beings exist in many other traditions. The Dwarves (Old Norse dvergar) are not always clearly separated from Elves (for instance, the Nibelungenlied features a Dwarf-king Alberich whose name means 'Elvenking') and often considered a subtype of the latter. Unlike the elves, which underwent far-reaching changes in folk tales after Christianization, the image of Dwarves remained more constant. Generally, Dwarves are imagined to be small humanoid beings living underground and showing high skill in the crafts, especially mining and metalworking. Dwarves are often perceived to have magical powers, like Elves.
Dwarves in modern fantasy fiction and games
The modern fantasy tradition of Dwarves is mostly based on J. R. R. Tolkien, who built his Dwarves on mythological models. He designed a conlang for the Dwarves named Khuzdul, which, however, is not as well known as his Elvish languages. The Dwarves of Middle-earth are mostly allied with the Elves, though Elves and Dwarves mildly dislike each other.
Examples of contemporary Dwarvish conlangs
Andreas Johansson designed a (yet unnamed) language for Dwarves in his own fantasy conworld.