Along with dedicated websites, statistics can often be found in so-called "grey" or "gray" literature: documents produced by governments, thinktanks, non-governmental organizations, and so on. Using Google to find these reports often works well.
A U Sask guide to data and statistics. Includes information on data sets (Canadian and international), analysis software, data visualization, and data management
Global disease distribution and outbreak maps, and lists of countries indicating their sanitary statuses. Also disease event reports, animal health status, veterinary services, population, vaccinations, etc. by country.