If you liked my Changing Gamers assumptions about Pathfinder (Part II, Races), consider this post a "Part III, More Races". Although originally intended to Pathfinder, I believe it works well for any fantasy setting (especially D&D-ish ones). It's kind of a mad (and very weird) brainstorm, actually.
I) Elves are all immortal, but just in body (that's why they have such a beautiful and young appearance, they're made to be the ideal of youth and perfection). However, their mad creators never did pay much attention to the spirit (and in fact didn't wanted to… you see, not competition). So, at exactly every 111 years, an elf spirit is replaced. The Elf just awakes one day without remembering his/her past "life" (oh, he/she knows how to speak and has some basic knacks, but just that). Elven clerics believe their spirits go to the gods after suffering 111 years here in the Material Planes (some heretics believe that every Elf is actually a god, temporarily banished to the mortal world). Elven wizards (and cynics) believe that their spirits’ accumulated knowledge and strength are consumed by their deities in order to maintain the pantheon's power. The real problem for an Elf is when he discovers that in a past "life" he was a terrible tyrant and that most human and dwarven kingdoms want him dead.
II) Dwarves are actually the Worms of Ymir, the primordial giant/titan/deity/Great Old One from whose body the world was made. The Dwarves were the first mortal beings and - not having any plant or animal life around to eat - devoured Ymir's flesh. Those first Dwarves became like their "creator" (except in size), humanoid creatures capable of cunning, magic and with great skills for crafting things of beauty – and an even greater gift for fighting (particularly against giants). The problem with Dwarves is that they still must consume carrion from humanoid corpses in order to retain the mind and body faculties. They do this in secret (although ghouls know that and consider Dwarves their "brothers in arms"). A Dwarf who refuses to eat carrion slowly becomes a pale and faceless half-worm/half-humanoid thing that, with time, grows to become a voracious and terrible monster.
|Did you remember that they looked like this?|
III) Gnomes, as you know, are actually children from other humanoid races (mostly taken from humans and halflings) stolen by the Fey to serve as their pets and slaves. Those Gnomes that you see around in the Material Plane are the ones who escaped the Fey Realm/First World/Arborea/Arcadia/Red & Pleasant Land. Each Gnomes dreams and can occasionally see their Fetchs - the fake copies left behind with their original mortal families. As old and fugitive children, many Gnomes try to destroy their Fetchs and return to their families. This rarely ends well (a few more disillusioned/mature Gnomes just check from time to time to see - secretly - if their loved ones are doing fine). All Gnomes also deeply fear their old Fey Overlords, who can still show up to reclaim them (yes, I'm totally stolen from Changeling the Lost).
IV) The first Halflings were actually normal animals that learned to speak and shapechange into their known humanoid forms. The learned the knack from their old master, the dreaded and mythical Hag Queen, ruler of the fallen race. Most Halflings, long ago, decided to leave their original homeland to flee from the Hag Queen. She used them as spies, to fetch human children for her to eat (or to raise as new hag, if females). (I know I promised "no mechanics", but if you liked this allow a Halfling to shapechange into one normal small animal, maybe through a Feat or after completing a Quest... or you can use this excellent take on Hengeyokai as a shapechange mechanic)
|An awesome book with horrible art...|
V) Orcs are known as the cauldron-born. They're the creation of dark sorcery, made from the corpses of the fallen, mixed with worms, mud and blood. That's why they're so savage, bloodthirsty and bestial. The ritual for making orcs always show up from time to time, usually in the hands of a dark lord, necromancer or mad wizard. Each new "recipe" for orc creates a different type of creature (all similar). Most free orcs want nothing more than destroying the ritual once and for all (or at least kill their masters). The fact that they're called 'Cauldron-Born' created some interesting folklore and jokes... if a food is particularly bad, you still can always hear someone taunting the cook by saying that "an orc will eventually climb up from that if you don't improve it").
VI) Half-elves are humans who sold their souls to the bound and buried Elf Kings. In exchange for a very long lifespan some humans sell their souls not to devils but to something far worse – the dread archfey of old, trapped beneath the hills and barrows. The new half-elf gains beauty, a little fey greatness (represented by their character class gifts) and a few good centuries to enjoy. In exchange they become the Knights of the Old Kings and must occasionally do their bidding.