Greyhawk: Descent into the Depths of the Earth
The Underdark concept originated in Greyhawk with the in the AD&D adventure module Descent into the Depths of the Earth, published first as two different modules in 1978, and republished in a compilation module in 1981. See Korvin's answer for more details about this one.
Matthew Mercer's world Exandria features an underdark, and is featured a few times in the Critical Role podcast. For canonical material, we see in Explorer's Guide to Wildemount that the Kryn Dynasty lived for a time in Wildemount's underdark before rebuilding their capital city:
Beneath the ruins of Ghor Dranas, a group of scavenging drow turned from Lolth, their primary deity for centuries, finding renewed faith in an esoteric entity they called the Luxon. Guided by the light of their new deity, the drow survived their ascent from deep within the Underdark and reclaimed the halls of Ghor Dranas for themselves, naming their new home Rosohna, or “Rebirth.”
Dark elves are the most populous race within the Kryn Dynasty. The drow were the first people to uncover the first buried Luxon beacon many ages ago, in a time before they turned from Lolth and escaped enslavement from the Betrayer Gods. The dark elves claimed the dread citadel of Ghor Dranas as their own, as well as the massive network of underground caverns that make up the Underdark of Wildemount. The Kryn are stealthily becoming a force to be reckoned with.
Eberron calls their underdark "Khyber", and it is featured in a section of Eberron: Rising from the Last War:
Any time someone descends below the surface of the world, they enter Khyber. But the underworld takes two very different forms. First is the natural realm, networks of tunnels and caverns formed from stone and soil. These passages are dark and dangerous, but they’re exactly what you expect to find in an underground realm. Such passages might be home to carrion crawlers, giant beetles, or clans of kobolds. But ultimately these mundane caverns follow the laws of nature.
There’s another aspect to Khyber: go deep enough and you find a seemingly endless array of demiplanes, each stranger than the last. When descending into a chasm, you could find a labyrinth inhabited by demons or discover a realm consisting of the guts of a colossal living creature. Anything is possible in Khyber, and these “worlds within” are home to all manner of terrors.