Tiamat is an evil queen-goddess of dragons. She appears as a massive dragon with five heads, each of which is of one of the five types of Chromatic dragon. Tiamat makes her Realm in Avernus, the first Layer of Baator. Tiamat is praised by evil dragons and their servants, and she is quite active in affairs on the Prime Material Plane as well as the Outer Planes.
According to legend, Gith traveled to Baator and struck a deal with Tiamat to establish an alliance between the Githyanki and dragonkind. Gith never returned from Baator, but the announcement of the alliance was carried out by a consort of Tiamat, the red dragon Ephelomon.
Tiamat's other major dragon-god counterparts are Bahamut, god of good dragons, Chronepsis, dragon god of time, death, and fate, and the rest of the Draconic Pantheon. She also has close ties to the Babylonian Pantheon.
Tiamat presently has five consorts, great wyrms of each Chromatic dragon species. Previous consorts include Apsu, Kingsu, the aforementioned Ephelomon, the red dragon Etiol1, and the now-undead dragon Dragotha2. Three of Tiamat's children were detailed in Dragon #260. An-Ur, the Wandering Death, wanders the Ethereal Plane, devouring whole Demiplanes. It supposedly sprang into being from Tiamat's first breath. Maybe she had a consort named First Breath, but An-Ur resembles no draconic species, except perhaps the ethereal moonstone+dragons. Dhakoth the Corruptor was born on the Negative+Energy+Plane. Its father is unknown. Mordukhavar the Reaver is the offspring of Tiamat and Cantrum of the Dark Eight. 3
Periodically she has new battles with Marduk, who dwells in Arcadia. She also battles Bahamut, her lawful good counterpart. Tiamat's emnity with Bahamut dates back to their creation, when Io made them; they were made with the intention of becoming complements and mates, but their personalities were too much at odds. Tiamat murdered Vorel, her eldest brother, and tried to frame Bahamut for the deed. Io realized who was truly to blame, though, and banished Tiamat from his presence.4
Tiamat's 3rd edition statistics appear in Deities and Demigods and her realm is described in the Planes of Law boxed set and in Fiendish Codex II: Tyrants of the Nine Hells. Tiamat's lair also plays a big part in Fires+of+Dis.
1. Epic Level Handbook, page 275
2. Dragon #134, also Dungeon #134
3. Dragon #359, page 68
4. Races of the Dragon, page 16