Okunoshima Island, Japan
What's up with Japan? A bazillion people live in Tokyo, but they never think to move out to these animal-overrun islands. It's weird. Actually, that's like the least weird thing in Japan.
Once a WWII poison gas production facility, the less than flattering history of this island has been transformed into a tourist attraction boasting hundreds (some even say thousands) of rabbits; these furry friends are obviously far more popular than the onsite Poison Gas museum. There's also a hotel, six-hole golf course, beaches, and camping grounds. Legend has it that these bunnies came from the facilities’ lab animals, which were let loose when it shut down, and then, well… reproduced as rabbits are wont to do. Party poopers, however, claim that they were brought there later, to attract visitors.
Bonus: Watch this video of a hapless tourist getting chased by a hopping herd of rabbits.