Subspecies are animal groups that are related, can interbreed, and yet have characteristics that make them distinct from one another. Two basic ingredients are critical to the development of separate subspecies: isolation and time. Unlike most animals, humans are a relatively young species and we are extremely mobile, so we simply haven't evolved into different subspecies.
The earliest hominids evolved from apes about 5 million years ago, but modern humans (Homo sapien sapiens) didn't emerge until 150,000-200,000 years ago in eastern Africa, where we spent most of our evolution together as a species. Our species first left Africa only about 50,000-100,000 years ago and quickly spread across the entire world. All of us are descended from these recent African ancestors.
Many other animal species have been around much longer or they have shorter life spans, so they've had many more opportunities to accumulate genetic variants. Penguins, for example, have twice as much genetic diversity as humans. Fruit flies have 10 times as much. Even our closest living relative, the chimpanzee, has been around at least several million years. There's more genetic diversity within a group of chimps on a single hillside in Gomba than in the entire human species.
Domesticated animals such as dogs also have a lot of genetic diversity, but this is mostly due to selective breeding under controlled conditions. Humans, on the other hand, have always mixed freely and widely. As a result, we're all mongrels: Eighty-five percent of all human variation can be found in any local population, whether they be Kurds, Icelanders, Papua New Guineans, or Mongolians. Ninety-four percent can be found on any continent.
Animals are also limited by habitat and geographical features such as rivers and canyons, so it is easy for groups to become isolated and genetically distinct from one another. Humans, on the other hand, are much more adaptable and have not been limited by geography in the same way. Early on, we could ford rivers, cross canyons, move great distances over a relatively short time, and modify our environment to fit our needs. We are also extremely mobile as a species. Even the remotest island tribe in the Pacific originally came from elsewhere and maintained some contact with neighboring groups.
We may think global migration is a recent phenomenon, but it has characterized most of human history. Whether we're moving halfway around the world or from one village to another, the passage of genes takes place under many circumstances, large scale and small: migration, wars, trade, slave-taking, rape, and exogamous marriage (marriage with "outsiders").
It takes a long time to accumulate a lot of genetic variation, because new variants arise only through mutation - copying errors from one generation to the next. On the other hand, it takes just a very small amount of migration - one individual in each generation moving from one village to another and reproducing - to prevent groups from becoming genetically distinct or isolated. Humans just haven't evolved into distinct subgroups.