Well, most recently, I added Whisper Gnomes from "Races of Stone". Since I'd banned halflings, they fill that basic role.
Hobgoblins are extremely militaristic and honorbound. They are LE to LN. One nation generally reveres the same god as paladins would (if I allowed paladins).
Trolls are, basically, the trollborn from the 2E "Viking Campaign Book". They are natural psions, but have a link to the plane of Shadow instead of the Ethereal plane. They are noted for being able to forge weapons from the shadowstuff that makes up the Shadow plane.
Yeti are, basically, evolved polar bears. Since no one has really expressed much interest in playing them, they'd remained vague, stat-wise. With "Races of Stone", I snagged the feral gargun stats to represent the Yeti, although I'll probably replace the high altitude ability with better cold resistance.
I've got a LA +0 race of feline tieflings, anthropomorphic wolves, fish-people, alabasts from MCAU, and evil super-strong Gnomes in my AU-rules homebrew.
IK has ogrun, basically ogres crossed with goliaths (who they predate); trollkin, an LA +1, super-tough lesser breed of trolls (IK trolls are way different from core, though); modified goblins, modified elves, and scads of human subraces.
Eberron has the kalashtar, warforged, shifters, and changelings.
When I decided to run the Shackled City adventure path from Dungeon, I decided that I would have the players create very different characters in order to offset the very standard dungeon crawl nature of the campaign. So I set down several rules, one of which was that each player must use EITHER a race OR a class not taken from the PHB when creating their (first-level) character. I also decided that whatever races the players chose would be the "Standard" races of the world, with the remaining PHB races being in the minority. So I ended up with a motley party consisting of a gold dragon (using the class from Dragon), a weretiger (using the class from Dragon), a half-celestial, an anthropomorphic ape, and a Green Folk (from Bastards and Bloodlines).
Unfortunately, the more I read the modules in the adventure path, the more I decided that it would be difficult to go through and replace all the elves and gnomes etc. in the path with these races. So, instead, I said that they were the dominant species on one continent but that they had traveled to another continent (populated by standard D&D races). But I did put together a lot of backstory for those races.
The weretigers are commonly known as fierce warriors and cunning rogues, combining the sleek and dangerous nature of the tiger to produce a culture that produces some of the best mercenaries and soldiers around. They live in family groups that often consist of multiple families under the same roof. Though they are fierce combatants, they are also very affectionate within their families and put home and relationships in a high priority.
The half-celestials are the dominant race of the Far Continent, replacing humans in that role. In addition to being the leaders of the religious institutions, they are also the primary agents of government and the law. They hold almost all positions of power and leadership, and their theocracy is strong, but fair. Many speculate that the vast half-celestial population and their strong society are the result of celestials abandoned on the Material Plane eons ago, and their descendants continue to pass on their bloodline and the benevolent laws of their ancestors.
The Green Folk are the dominant barbarian tribes of the Far Continent, and have resisted, though peacefully, the organization of the half-celestial society. Though the Green Folk tribes are scattered and continue to fight amongst themselves for land and prestige, they provide safe haven and travel through their lands to those who live under the half-celestial rule thanks to an ancient pact between the founders of both societies. The Green Folk are hardy and tough, and their warriors are fierce and fight to the death. They care little for religion and tend to focus on the practical side of things. They have a very rigid caste system which places station above almost all other considerations, though mobility (both upward and downward) within the caste system is possible based on deeds.
The anthropomorphic apes (called "simians") are the only non-PHB race common to the world in the party that is not native to the Far Continent. They live in tribes in the jungles just to the south of Cauldron. They are much like the ape tribes in the recent Tim Burton Planet of the Apes movie. They share the jungle with tribes of Litorians (from Arcana Unearthed) and are bitter enemies with the newly-discovered werebaboons who have slowly begun to infest the jungle.
The gold dragon is the only surviving member of his species....as far as he knows. There are no other dragons in the world as far as he knows. I've replaced the dragons in the early modules with drakes, dragonnes, etc. instead. I've always believed that dragons should be both rare and very special, so this is my way of dealing with it. I'm leaving in two dragons...
the dracolich from Secrets of the Soul Pillars is going to be one of his ancestors gone bad, while I'm leaving Hookface in as one of the last surviving dragons.
I'm setting up the story of what happened to all the dragons as a driving theme of a possible Epic-Level Campaign.
I have contemplated having a race of "Gurgis" based on Lloyd Alexander's character of the same name (although in the Chronicles of Prydain Gurgi is unique).
I have also contemplated adding a race based on Phantasy Star's Myau the muscat:
These two "races" would take the place of halflings and gnomes, whom I dislike immensely.
Currently I am using the AU races -- litorian, sibeccai, verrik, faen (now in 3 flavours!), mojh (modified to be a true race, not just transformed humans) and akapans (my name for the giants).
On the main continent: trolls (which are more orc-like, though). I nicked the ideas for mojh and sprytes (more fey-like, though) from AU, with the fey being a possible transmutation for elves.
On a southwestern continent that is not much developped, there's some catlike race resembling pretty much the Dirdir von Vances's "Planet of Adventure" (my elves have aspects of the Pnume from the same source, btw). This means, they see themselves as the crown of evolution, but have some savage traits like ritualized hunts on sentient beings.
There are very few other sentient races, but most of them cannot talk with humans, elves or trolls (incompatible "tools" for speaking) and are, therefore, no choice for PC's.
The races from AU are core in my campaign with the races in the PH being considered exotic and rare - so they are actually the non-core races
But in addition to that I use the changeling and a half-fey homebrew race.
Characters also have the option of using ceremonies to unlock hidden bloodlines, this allows them to take "levels" in prestige races like celestial, tainted, fey, giant paragon, and of course the spryte and mojh.
I have quite a few odd races that I've either included myself, or have allowed to be added in some of my campaigns. Most are indeed non-core:
Javarran - Race of wolf people (see icon) that is something like the lupin, but a little more broad as a culture and with absolutely no ties whatsoever to a Lycan bloodline. They are one of the old races, and strangely, one of the very few 'naturally' evolved races. There are four sub-races: Khavijas (Wild), Khemruh (High), Winter, as well as the Dhuunir (True ones).
Centaur - A few sub-species of these as well. Extremely rare since they have been disappearing from the world with some of the other races bing pushed away by Dwarven expansion.
Raakiran - A player created race. My only rule on player created races was that they had to have at least a well thought out background. These are another 'animalist' race, having something akin to raccoons or other small critters. They are a cursed race each seeded with a demonic 'consciousness' infused in their bloodlines. Thus they are rarely used as PC's.
Litorian - I rather liked the write up they got in AU. I simply gave them tails, and meshed them more into my homebrew world.
Tanzians - Another player created race, and the oldest non-core race I've had in my campaigns next to the Javarran. Tanzians are akin to those of Nordic descent, and seem to embody the people of legend in that genre. They are keepers of arcane secrets of arms and armor construction.
Yinnapshai - A co-created race that I've really come to like. Their background is rather long and complicated, but in short, they were the forgotten and long dead people of the God Set, and resembled dark jackals. They were raised by Set and are now rebuilding their empire on a desert area taken over by human trading posts and ports. Lots of war there.
Lorrnath - I got tired of races of felines that kept getting thrown at me. I'm cool with that sort of thing, but it just got to be too much with this, so I went in an utterly opposite direction, and created an 'evolved equine' style race that had mixed histories, and are actually powers in merchant trading (Something like ancient romans with a more medieval feel).
Others have included critters such as Avariel, Wild Gnomes, Dryads, and a few others I can't quite recall.
