Medieval Europe
During the Crusades, Asian black rats began migrating into Europe in ever-increasing numbers. They brought along the fleas that carried the bubonic plague, which devastated Europe. Their numbers became so overwhelming that the profession of rat-catching had to be invented to deal with them.
Australia
When explorers began traveling to Australia, they inadvertently brought mice with them on their ships. The mice, facing few natural predators and plenty of easy food, began to rapidly reproduce, and to this day they are found in tremendous swarms. Mice are responsible for millions of dollars in lost crops each year.