Diseases are caused by pathogens which find a host to feed on. Usually, different living creatures will have different pathogens affecting them. Let’s consider animals – there are plenty of infections they experience, but the pathogens causing them are usually contained within a species. Even within the same species, different breeds can react differently to the same pathogens. For example some monkeys could be natural host (disease reservoir) for a specific disease and naturally immune to it, while other monkeys can die after getting infected with the pathogen.
Not all the viruses are transmissible between different species. The ones which are caused by pathogens which can transmit from animals onto humans are called zoonotic pathogens. We don’t know how many of animals’ pathogens are transmissible to humans, primarily because affected wildlife usually do not come to close contact with humans too often. But some estimates show that there are potentially 1.6 zoonotic viruses (this excludes other pathogens). Out of this viruses, which can all infect people, only 260 are so far known.
A few prominent examples of zoonotic viruses that humans experienced so far are Ebola (believed to come from monkeys or bats), HIV (monkeys), anthrax (grass-eating animals), Lassa haemorrhagic fever (mice), and a series of flues (such as bird or swine flues).