Race does certainly exist. But mainstream science today (with a political agenda) denies this fact (and ignores the principles of biological evolution).
Where do I begin...
Today mainstream scientists adhere to the "clinal" model of race. The clinal model holds that phenotypic changes (physical appearance and facial feature changes) are the result of adaptation to particular climates. Generally they divide "clines" into categories such as tropical, temperate, arctic, etc.
Yet there is a fallacy in this reasoning because the "races" do not correlate with this proposed geography. For example, one could walk on the steppe from Romania to Manchuria, where the climate is generally the same throughout. But the races along the way differ tremendously. To the west you have purely Caucasoid people and to the east you have purely Mongoloid people (East Asians). Other examples can be given for arctic and mountain regions also. Not all arctic people look the same. They can range from fair-skinned and blonde-haired, blue-eyed, sharp-featured Scandinavians and Lapps to swarthy and dark, flat-faced Inuit.
Another problem with the clinal model deals with definition. By definition, a "race" (or species if you will) is a breeding population. After a period of isolation, the breeding population develops unique traits that distinguish it from other groups. These distinguishing racial traits are clearly seen by everyone. And regardless, saying race does not exist due to clinal continuums is similar to saying species do not exist because we have complete fossil continuity.
Some scientists today also assert another fallacy and say that there is more genetic diversity within races then between them. Genetic research by plenty of credible and highly respected biologists disagrees with this claim. Of note is the work of Luigi Luca Cavalli-Sforza, one of the premier and pioneering geneticists. In his book, The History and Geography of Human Genes, Cavalli-Sforza outlines "breeding populations" throughout the world and plots genetic distances between groups. Ironically enough, Cavalli-Sforza also repeats the no race mantra, which is contrary to his entire book. This is just to please the media and ensure that his funding doesn't dry up!
Race is a reality. There are five races -- Caucasoid (Caucasian, White), Mongoloid (East Asian, South-East Asian), Negroid (Black, Sub-Saharan Africa), Capoid (Kalahari Bushmen, Hottentots), and Australoid (Australian Aborigines). Each race characterizes some period of human evolution, and may also represent a period of human migration.
There are physical differences between the races beyond skin color. Facial and nasal structure, jaw structure, prognathism, body proportions (arms, legs, torsos, even to hands and fingers), lung capacity, muscle build, body build, and even intelligence (but that is a nasty debate, so I don't want to go there).
The theory of evolution applies even to humans (yes, it is true). To think we could evolve from apes, spread around the world, remain geographically isolated for many thousands of years and STILL be "exactly the same under the skin", equal, etc., is false and contradicts nearly every law of biology.
Egalitarian politics has been of great hindrance to the study of human differences and diversity. Science must be objective and rigorous. It must not be tainted by political ideologies.