One-to-one nation states may be rare, but they aren't unheard of by any means.
Japan is probably the best example of a nation-state you'll find in this
mortal coil, with its own unique
everything. Not perfect—there are minorities, and there is a
diaspora—but very, very close.
If Korea were unified, it would be up there with Japan. Thailand, Laos, Vietnam, Cambodia, and Indonesia are other good examples in Asia. In Europe, things blur a bit, but I would count Greece and Iceland as good examples. Hungary and Bulgaria might count, too, but don't quote me on that.
In the Western Hemisphere, nation-states are rarer: in Latin America, the Hispanic populations share space with the Native American populations, and in North America (at least outside of Utah), everything's pretty much an ethnic mess. Haiti is probably the best example of a nation-state to be found in our half of the world, if a horrid example of a state.
With globalization going on as it is, the nation-state is quickly becoming an endangered species, and leaving us with a plethora of nationless states and stateless nations.