Chimpanzees

That is hard to answer with certainty. Prof. Robin Bernstein of George Washington University says that it might be possible in a lab setting, but there are three barriers to this happening in the wild: 1) humans and chimps would not normally look at each other as mates; 2) the biological mechanisms of human and chimp sexual reproduction are not exactly the same; and 3) There are great differences at the chromosomal level. I will go over each of these. First, animals tend to mate with their own species. This is because they are genetically programed to detect certain bodily attributes or hormones that make the males or females of their species attractive. In addition, species that are active in different areas tend not to come in contact with each other. So the chances of a male chimp and a female human or a female chimp and a male human finding each other attractive and mating in the wild is very slim. However, chimps raised as human children have been shown to be attracted to humans. See the question "Could a chimp mate with a human?" for more information.

Second, although both have similar reproductive systems, they are not exactly the same. For instance, chimpanzee penises are very long for their body size, but they are carrot-like in nature (i.e., it is wide at the base and tapers to a point). Human penises, on the other hand, are wide at the base and have a wide head. This means a chimp penis might not be rigid enough to reach far enough inside a human female to implant seed. The human penis might be too big to reach far enough inside a chimp female to do the same. It is important to mention that humans have forward-facing vaginas, while chimps have backwards-facing vaginas. Humans can have sex face to face, something that chimps can't do. Considering that chimps must mate in an awkward "doggie style," a human male might have problems orienting himself. The male chimp may have similar problems.

Third, chimps have 48 chromosomes (2 pairs of 24) and humans have 46 (2 pairs of 23). It is known that human chromosome 2 is simply a fused version of the chimp chromosome, which accounts for us having 2 less chromosomes. Animals with different chromosome counts can't usually mate, but there are a few instances where they have. For example, horses have 64 (2 pairs of 32) and a donkey has 62 (2 pairs of 31), but yet they are able to produce a mule. Since the mule gets an unequal number of chromosomes from both parents, it is born sterile due to genetic abnormalities. Therefore, if a chimp-human hybrid could ever be brought to term, a male specimen could never reproduce. Yet, there is evidence that human ancestors and chimps might have interbred in the past.

The oldest fossil associated with the human lineage is around 7 million years old. This means the joint human-chimp ancestor probably lived around this time. Yet, genetic chronology shows that the split between the lineages happened around 5 million years ago. In his article "Two Splits Between Human and Chimp Lines Suggested," science journalist Nicholas Wade describes genetic research that reconciles the difference by positing the separate human and chimp lineages might have continued to breed and later split for a second and final time. Genetic chronology shows that the X chromosome in the human and chimp lineages split over a million years before the other chromosomes. Dr. David Reich of Cambridge, the head researcher on the project, suggests this could have been caused by hybrid females interbreeding with chimpanzees (since hybrid males would not have been able to reproduce). In addition, he further suggests that this interbreeding could have hastened human evolution since it would have allowed us to better adapt to the new environment of the African savannah. Paleoanthropologists like Dr. David Pilbeam of Harvard are not quick to accept the information since genetic chronology only provides "relative ages, which are translated into real time by reference to a timescale established by early ape and monkey fossils." Further research is needed to determine if the hybrid theory is correct.

The Russian biologist Ilya Ivanov tried for 4 years from 1926 to 1930 to produce a Humanzee in a lab setting. He initially gained permission from the French government and backing from the Soviet government in 1925 to start such experiments in Kindia in Guinea (northeastern Africa), but none of the chimps assigned to him a year later where sexually mature enough to carry children to term. He then relocated to the Guinean capital of Conakry in late 1926 to capture his own specimens. He artificially inseminated three female chimps with human sperm in early and mid-1927, but none of them became pregnant. After returning to Russia in 1929, he gained permission and backing from the Soviet government to conduct human trials. But after the 1929 election changed the USSR's power base, Ivanov's experiments were stopped and he was eventually arrested and exiled. To my knowledge, no one has tried (legally or otherwise) to create a Humanzee since then.

Barring the natural barriers mentioned above, I believe there might be a psychobiological explanation for why Ivanov's early batch of chimps did not become pregnant. Ivanov captured wild chimps and then confined them to cages. One was even shipped from Africa to France by boat. Prof. Roger Fouts mentions in his book Next of Kin: My Conversation with Chimpanzees (1997) that such stress can cause adverse effects in chimps like hair-pulling and self-mutilation. Stress-induced chemicals like alpha-amylase have been shown to reduce a human woman's ability to become pregnant because it slows the descent of the egg. So it's possible that the stress from being confined to cages may have kept the chimp egg and human sperm from meeting. If he had used human-raised chimps who lived in spacious modern facilities, he may have had a better chance of succeeding. There is no telling what would have happened if the human trials were carried through.