I believe just about every race would exist, and be cultured in some part. Just as you still have native man living in the far off places of the world, so to you would still have pockets of mythical beings here and there.
Kobolds: The lizard rat to the uninformed, these creatures are actually highly industrist, highly magical, and the favored servants of the strongest creature, the dragon. I could see these crafty little shits getting jobs in mining and industry. Working along side dwarfs as they hollow out mountains. Their skills with traps can easily be turned to less lethal machines, being small they can create some pretty delicate machinery. You would still have the sewer dwelling savages, but they would be like packs of wild dogs, hunted down ever so often.
Goblinoids: I would see goblins being wiped out, their stupidity and small frames leading to their demise. Hobgoblins, being smarter, stronger, and more apt at creating cultures of their own, would be city states at start, warring with humanity and the other humanoid races, but after a long enough time, they would be absorbed and live like any Joe Blow. Bugbears would be cheap labor, and good for brutal sports.
Orcs: A bit dim, but still capable to form society. They would be more of raiders in the early years, but as time progressed they would eventually be tamed for a most part. Terrorist actions by those who "Remember the glory days" might happen, but for the most part they intergrate.
Ogres/Giants/Trolls: Strong, dumb, and hungry, I see them filling the roll of back room stockers, burger flippers, and other menial jobs. Just let a troll work at your fast food joint, and you don't need to pay him as much, he takes part of his pay in whatever gets thrown out. Sports, oh yes.
Dwarves: Jews. All I gotta say. They love money, have money, and are willing to let you take a loan. But be sure to pay them back, or it's your knee caps.
Gnomes/Halflings: House keeping!