For more information, read the excellent Plagues and Peoples by William H. McNeill.
Hinduism: The Caste System and Sacred Cattle
The caste system is an inherent part of Hindu culture (see the wonderful node by birdonmyshoulder* and mattbw caste system for more information). Many theories exist as to how it was formed, and one of them is that it was a response to the epidemiological disaster that occurs when two cultures who have never had contact with one another meet. This is seen time and again throughout history: two cultures collide, each with their own set of diseases, and infect each other. Large die-offs occur, and either assimilation or destruction is the outcome. In the Indian subcontinent, far in the past, the Aryans invaded and began to interact with the native people. Both cultures had distinct sets of diseases. Rather than go through the cycle of infection and destruction, they formed a system of separating the two. Over time, this became the elaborate caste system.
In the ancient world, and today, animals are often the bearers of disease: witness Mad Cow Disease, the Black Death, salmonella, trichinosis, possibly Ebola, possibly AIDS... Indian culture evolved so that eating meat-- often infected-- became taboo. This evolution was presumably the result of observations over time: people who ate meat often had more diseases than people who didn't. This practice continues today, and no doubt still saves lives from disease.
Christianity: Hope in a time of Great Suffering
Christianity is a system of thought and emotion completely adapted to a world full of poverty, hardship, disease, and violent death. God's omnipotence-- and stories such as those of Job-- made life more meaningful in the face of tragedies. In a world where one could be healthy one day and dead of a terrible accident or disease the next, the thought that an afterlife free from suffering was the ultimate goal was highly reassuring. Also, one could envision one's relatives in that warm, healthy heaven already, even if they had died terrible deaths.
The early Church was formed in cities: Jerusalem, Antioch, Rome, Alexandria. In a city, the risk of disease is immense, because of poor sanitation and the sheer mass of undernourished, unhealthy people living together. Thus, for a young religion trying to find recruits in these cities, the belief system had to offer release from suffering. One interesting "selling point" that Christians had was that their Bible preached care of the sick. Before Christianity came on the scene, the sick were often abandoned out of fear; the early Christians, while having a high death rate due to infection, were less afraid to die because of their belief in an afterlife of eternal happiness, and would therefore look after those stricken with disease. So, conversion to a religion where one could be looked after in a time of disease became highly desirable.
Christianity might not have become the major religion it is today without its foundations in Rome at that particular time. As Rome fell into decline, more diseases began to ravage it. Invaders carried new pestilences, and in the cities (and to some extent the countryside) there were the ever-present threats of plague, smallpox, anthrax, and other diseases. The Christian system of belief was infinitely more hopeful in a world of suffering than the earlier, pagan beliefs.
Buddhism: Transcendentalism and the Asthetic's Life
Transcendentalism is a perfect belief for a poor, disease-stricken society. Unlike Confucianism, which was a political religion, Buddhism was a spiritual one advocating an apolitical belief system: don't live in the material world, which is full of suffering; instead, live in self-denial to achieve a more perfect afterlife. By surviving on very little willingly, a person not only can escape more diseases (such as those passed through meat), but also live in a culture that has very little food to share.