Guide to The Lord of the Rings/Races/Balrog

Physical Description
Tolkien had changed the specifics overtime, but Balrogs retained many notable characteristics. They are large, muscular humanoids, with black bodies and usually flames coming from bodily parts (Mostly the head). No mention of clothes or armor is mentioned with the Balrogs, but they are noted to wield a variety of weapons, including flaming swords, flaming whips with many thongs, and blackened maces and axes.

Other interpretations are based on comments Tolkien had made throughout his texts, with Durin's Bane considered "a thing of slime" after being quenched in the waters below Moria. The biggest discussion is on whether or not Balrogs had wings (Or were capable of flight.), as Tolkien had used both metaphor and description to describe the wings of Balrogs, and alternating on the same page:

"His enemy halted again, facing him, and the shadow about it reached out like two vast wings." —The Lord of the Rings, II:5, "The Bridge of Khazad-dûm"

and

"...suddenly it drew itself up to a great height, and its wings were spread from wall to wall..." —Ibid.

Like most discussions, the image is mostly up to interpretation of the readers, and either description appears to be correct as the other. Without Tolkien himself to mediate, it is possible that the discussion will continue as long as Tolkien has readers. Visual interpretations tend to follow the Winged argument, and present Balrogs with wings, though often unusable for flight.

Notable Balrogs
Across Tolkien's Legendarium, there are very few Balrogs of note, and only one was named. (May contain spoilers)

Gothmog
Gothmog was mentioned in the Quenta Silmarillion, and took part in some of the battles that took place, primarily the Second (Dagor-nuin-Giliath) and Fifth (Nírnaeth Arnoediad) battles. Gothmog itself is Sindarin for "Dread Oppressor"

Durin's Bane
During the Third Age, the dwarves in Khazad-Dum had delved to deep in their search for Mithril, and awoke the sleeping Balrog below. Known only by titles given to it by others, such as "Nameless Terror", "Flame of Udun" and "Durin's Bane", the Balrog had killed many in Khazad-dum, including Durin VI and giving him the name "Durin's Bane" when he awoke. He was finally finished after a fight with Gandalf beginning at the Bridge of Khazad-dum and ending atop a peak inside Durin's Tower.