The race of the ancient Egyptians has been the subject of heated debates for centuries now. At the beginning of the modern age, European thinkers argued that the ancient Egyptians were white, generally due to the racial stigma surrounding those of darker skin tones at the time. Afro-centrists, on the other hand, contend that the ancient Egyptians were, indeed, black. The truth is, we don't really know the definite answer to the question of the race of the ancient Egyptians, but we know enough to know that, like modern populations, skin color varied amongst the peoples of Egypt in ancient times.
Geographically, Egypt is the border between African and Asian lands. Its unique location allowed for a mixing and mingling with people who spoke many different tongues, and whose skin tones spanned the colors of the human rainbow. We know without question that the people of Egypt were African; however, that doesn't necessarily mean they were black.
To really ascertain what race the ancient Egyptians were, scientists have to reach very far back to the times of the Old Kingdom and the Pre-dynastic period where racial mingling was less common. Analysis of skulls and bones from that time conclude that the Egyptians of that period exhibited traits linked with Caucasoid, Negroid, and Asian peoples. In the 1970's, studies were done to test the melanin content of mummies. The higher the melanin levels, the darker the skin would be. However, the tests proved inconclusive.
The age of the New Kingdom was full of migration. People flowed in and out of Egypt like water, and the Egyptians married foreigners with skin both lighter and darker than their own. It was during this time that foreign blood may have very well leaked into the royal family itself.
Two of Akhenaten's wives, Nefertiti and Kiya, are believed to have been - or descended from - princesses from Mitanni. The race of the people of Mitanni, particularly the royal family, is thought to be Indo-Aryan. It's become commonly believed that Tutankhamen was the son of Akhenaten by Kiya, so he, too, would've been of some slight Indo-Aryan descent, were that the case.
Migration rates exploded during the Hellenistic period, after the death of Alexander the Great. His Macedonian heirs, the Ptolemies, took control of the kingdom. It's been widely argued that Cleopatra VII, the last pharaoh of Egypt, was black. However, she was a Macedonian Ptolemy. It's been suggested that her grandmother was Persian, which might have made her skin tone darker than many of the Greco-Egyptians of the time; however, she wasn't black.
Descriptions of ancient Egyptians by their foreign contemporaries varied. Some Greeks referred to their appearance using terms like "black-skinned" and "woolly-haired"; however, other Greeks referred to them as looking like the lighter skinned populations of the Indian subcontinent. Because of the widely different depictions, it's safe to assume that by the time Egypt and Greece had contact, Egyptian peoples looked very different from one another, possibly due to the extreme rates of Egyptian trading and travel at the time.
Throughout archaeological sites in ancient Egypt is evidence of the way the Egyptians viewed their foreign neighbors. There's a wall painting in the tomb of Seti I that depicts a Syrian, a Nubian, and a Libyan next to an Egyptian. It should be noted that the Syrian and the Libyan were portrayed as Asiatic, whereas the Nubian was painted as having very dark, almost black, skin. The Egyptian, on the other hand, was depicted as somewhere between the two extremes, with skin of a reddish brown color. In fact, the ancient artists, in their scrupulous detail, went as far as to take care to realistically portray the different facial structures of the men depicted. Even through the face, it's clear that the Egyptian looks different from the other three.
What we can say about the race of the ancient Egyptians is that they viewed themselves as a race separate and superior to any other, the Egyptian race.