There is certainly room for that in some settings, especially those built from scratch with those assumptions, but many of the races that made it into 4th Edition were prefigured as much rarer races in various 3.5 splatbooks.
Personally, I'm all for PCs being from species that are rarely seen in the world, without having a whole district in a major city devoted to others like them.
While I was following that line of thought, I was wondering what could make some species less common, and it led me to a couple of new (or slightly reworked old) origins. If you happened upon my post about this on Google+, hopefully you will find some value in the more fleshed out version of the concepts presented here.
Dragonborn (Cursed by the First Dragons)
The linnorm are an ancient family of dragons, more primordial than the chromatic or metallic dragons that spring to mind when most sages speak of things draconic. The linnorm are mysterious, ancient, and in many folk tales are associated with curses.
The Dragonborn are the children of adventurers who plundered the hoard of a linnorm. Unless adventurers either undertook their quest against the linnorm in the name of a god, or found a priest in good standing to properly bless and cleanse the adventurers in question, the children of those who raided the linnorm's lair may be born carrying part of the linnorm's spirit.
Dragonborn can vary greatly in appearance, depending on the whims of fate and the nature of the linnorm whose treasure was plundered. All Dragonborn bear obvious reptilian features that are difficult to hide, such as scales, unnatural eyes, horns, or fangs, or all of the above. Some dragonborn may be born with two legs, but many have the same serpentine trunk that is native to linnorm.
Nothing short of a wish can change the child's species back to that of the child's parents once the child has been conceived. If the plunderers have not been cleansed before this time, the child is now and forever a Dragonborn. Dragonborn themselves cannot have children.
Linnorm can sense exactly what a dragonborn, no matter what the disguise they may be using, and will attempt to slay the thief-spawn abomination on sight.
Dragonborn with this origin function in all ways as Dragonborn described in the Player's Handbook.
Hellbred (Tiefling Alternate Background)
Note: Hellbred first appeared in the Fiendish Codex II: Tyrants of the Nine Hells.
Some souls that are damned get a second chance. Sometimes that second chance isn't to redeem themselves, but rather, to further the cause of Hell on the material plane just a bit more before final death can claim them.
Hellbred are beings that have died and would be sentenced to the Pits of Hell, but they are singled out to return to life, but changed. Often this is because the Lords of the Nine have a purpose for that being, something they hope one particular being is suited to perform above all others.
Hell does, however reluctantly, follow some semblance of order, and in order to allow mortal beings bound for Hell to return to the world of the living, the Upper Planes decree that the soul returned to life must have the chance at redemption. Thus, the Hellbred is a living wager between Hell and the inhabitants of the Upper Planes.
At some point in their new lives, and sometimes at multiple points, Hellbred receive a vision of what Hell wants to accomplish through them. The vision is usually accompanied by some promise of lessened suffering in Hell. Sometimes, if the Hellbred has formed a bond with others in the land of the living, these visions are accompanied by promises of torture and ruin for those the Hellbred cares about. Regardless of the accompanying message, the visions are not compulsions, and cannot be, due to the nature of the agreement with the Upper Planes.
If the Hellbred dies in service to a deity, or has become an exemplar of good, Hell no longer has a claim to their soul.
Hellbred always have some obvious, very difficult to disguise mark, sometimes several, to distinguish them as the property of Hell. Some have glowing Infernal sigils on their face, glowing red eyes, all black or all white eyes, horns, hooves, tails, bright red skin, or any combination of the above.