Summarizing this one. Can use some more opinions.
Somehow I missed this Natural category. Here are ones I'd vote for (keeping in mind that for me some of these are pulling double-duty as representative sites for flora or fauna around the world):
1. Dja Faunal Reserve -- rainforest in west-central Africa which includes wildlife like the western lowland gorilla and the forest elephant
2. Rainforests of the Atsinanana -- highlights wildlife endemic to Madagascar, including lemurs
3. Dong Phayayen -- Southeast Asian forest home to elephants, tigers, leopard cats, and the Siamese crocodile
4. Tropical Rainforest Sumatra -- Indonesian rainforest which is home to the Sumatran orangutan, rhinoceros, elephants, tigers, and Malayan sun-bears
5. Jiuzhaigou Valley - old growth forests in central China
6. Central Sikhote Alin -- covers a temperate zone from taiga to subtropics in eastern Asia, and is home to the Siberian tiger and Himalayan bear
7. Yakushima -- warm temperate forest home to the Japanese cedar
8. Gondwana Rainforests -- rainforests in eastern Australia which are home to a variety of marsupials, including kangaroos, koala, and platypus
9. Tasmanian Wilderness -- temperate Australian wilderness with variety of marsupials
10. Great Smoky Mountains National Park (Natural Landscape, Forest category) -- highlights wildlife from the Appalachian Mountains of eastern North America, including black bears, red foxes, white-tailed deer, raccoons, and a variety of salamanders
11. Redwood -- iconic giant trees on the west coast of North America
12. Belovezhskaya Pushcha / Bialowieza Forest (how exactly isn't this in the Forest category?!?
) -- woodland in north-central Europe, home to wolves, European bison, lynx, and otters
13. Laurisilva of Madeira -- largest surviving area of laurel forest
I have no choice for South America on this list since I'd vote for the Brazilian Atlantic Islands (Marine/Coastal category), Noel Kempff Mercado National Park (Diverse Ecosystems category), and Huascaran National Park (Mountains category).