I'm going to take a bit from my homebrew world, Tor-eal.
Yikkan Goblinoids: Long ago (over a thousand years ago), the Weave of Magic was shattered by a tremendous catastrophe that resulted in the death of the Goddess of Magic and much of the rest of the pantheon (it's a bit more complicated than that, but this is a basic rundown). The Weave was splintered and caused magic to be much more . . . "interconnected" might be the right word. Basically, instead of being neat and tidy, magic is much messier and has a greater affect on its surrounding environment than before, kind of like Dark Sun, but with different kinds of magic affecting its surroundings in different ways (necromancy kills plants, evocation destroys a bit of the land-scape, abjuration makes materials harder temporarily, transmutation changes the color of the grass or leaves, conjuration might summon a noncombatant creature for a bit, etc).
This new source of magic took centuries of hard-study by the inhabitants of the devastated world to begin to understand, the foremost researchers being the newly reorganized goblinoid society, with hobgoblins taking charge of understanding the nature of the newly reformed magic system. The goblinoids dubbed the new source of magic the "Yikare", meaning "The Three as One" in the goblin language (with "The Three" being the different types of magic; arcane, divine, and primal). The goblinoid culture began to worship the Yikare, receiving magic in return for their faith, eventually granting the Yikare a spark of divinity, but not sentience. The highest-ranking worshippers among the Yikare's goblinoid followers tapped into powerful magic that allowed for them to transform into arcane angels, a Hobgoblin Abjuration Wizard with arcane-blue wings, a Bugbear Arcana-Domain Cleric with radiant-yellow wings, and a Goblin Divine Soul Sorcerer with shamrock green-wings. The new goblinoid society now is devoted to the spreading of magic across the world and ridding the world of psionics (which they believe mutilates magic and prevents the world from becoming its true self), now spread across the globe through an internationally connected faith-group known as the Yikkan Contingent.
In the Yikkan Contingent, the Bugbears typically serve as the priests and holy-warriors of the faith (Arcana, Life, and Knowledge Domain Clerics, as well as Paladins), the Hobgoblins serve as the arcane scholars and professors of magic (Wizards, Eldritch Knights, and occasionally Artificers), and the Goblins are the charismatic spokespersons, magicians, and scouts (Divine Soul Sorcerers, Celestial Warlocks, Swashbuckler Rogues, and Bards).
Felshen: On the island of Lantanea, a group of artificers known as the Pre-Genitors, composed mostly of gnomes, dwarves, and humans, decided to set out and achieve what was thought to be impossible: creating a unique race of fully-reproducing people (these same artificers had created a non-reproducing race before, the Golmeng, who are basically this world's version of Warforged, but as Golemkin with subraces made out of different substances, with stone, metal, clay, glass, and crystal Golmeng as the main subraces). After over a century of experimenting, by growing alchemically-enhanced flesh in laboratories with a mixture of dwarven, human, and elven DNA, creating their magically-enhanced brains to make the race intelligent, and giving the race distinctive and bright skin-colors to stand out, the Pre-Genitors eventually succeeded at their goal. Originally called "Fleshlings", as a subrace of the Golmeng akin to Flesh Golems, the Felshen quickly adapted to become an autonomous and fully-reproducing race of highly-intelligent people. With no true place in the world, many Felshen left their home-island to discover what the rest of the world had to offer.
A group of Felshen that was out looking for a place to call their home came across a rare type of dragon, a Sapphire Dragon that discovered the true potential of the Felshen. This dragon, only ever referred to as "The Founder", taught the Felshen that their magical nature and enhanced brain-chemistry made them uniquely suited for learning psionics, so much so that the potential was locked away in their brains just until the Founder removed the barrier and taught the Felshen how to master their psionic powers. Quickly spreading the psionic art across their people, the Felshen became devoted to unlocking all the secrets that the world had forgotten throughout the ages about the power of psionics, now known in their language as the "Shei", or "the Mind" in Common. Copying the strategy of the Yikkan Contingent and abandoning their hope to find one true land for their people, the Felshen decided to spread across the world to eventually unite the world in the art of psionics, this organization known as the "Sheiohn Foulen", which means "The One-Mind Foundation". The Sheiohn Foulen accepts any who can speak telepathically or that has some basic psionic powers, such as the Gith, Verdan, Ghostwise Halflings, Gemstone Dragonborn, and Jemlin Golmeng (crystalline golemkin with psionic powers that the Felshen helped create). The Sheiohn Foulen and the Yikkan Contingent are sworn rivals, having a sort of holy war between them that has lasted for centuries, and recently forced to a stalemate due to the intervention of the bystanders. The Yikkan Contingent refuses to acknowledge that the Felshen have souls, seeing them as abominations that pervert the natural order of the universe, and the Felshen are mostly out for revenge due to the persecution that they have faced at the hands of the Yikkan Contingent and also because their ideals of a "perfect world" are in direct contrast to that of the Yikkan Contingent.
The Sheiohn Foulen is interconnected throughout the world using magical gemstone beacons that allow them to increase the range of their telepathy (making use of
Psi Crystals), using chains with towers of these psionic beacons wirelessly connecting different settlements of the Sheiohn Foulen to one another through these innovations (whereas the Yikkan Contingent uses the Sending spell to communicate with one another at long-distance). The centers of their settlements contain a crystal tower that serves as a library for the collective knowledge of the members of the Sheiohn Foulen that anyone with telepathy can connect to and write in (kind of like a limited psychic version of the internet for this fantasy world). The settlements of the Sheiohn Foulen are filled with a diversity of people, with Felshen as the main race populating them, but also filled with Gemstone Dragonborn, Jemlin Golmeng, and the occasional Verdan, Gith, or Ghostwise Halfling. Felshen come in a variety of colors, most often being turquoise, cyan, magenta, or deep-purple, but there are also more rare colors, like yellow, cream-orange, lime-green, ivory-white, or obsidian-black. Their hair-color varies as much as their skin-color does as well, especially on an individual basis.
Well, those are four non-standard races that are a major part of my world (yes, one of them is homebrew, but they're very similar mechanically to the Kalashtar, and I've seen a few others in this thread use homebrew/non-official races. I hope that's okay, though).