What animals are illegal to hunt for?

There are a number of factors which determine whether hunting for a particular animal is illegal:

First, where is the animal? Its entirely possible that its illegal to hunt an animal in one country, but cross the border a few miles away and its perfectly legal. The same goes for which state or county are you in if you're in the US.

Second, is it in season? You can hunt deer in many places in the US but only durig the pre-determined period of time (usually fall/winter)

Third, is it specifically protected by any laws? Some animals are protected by the Endangered Species Act and it is always illegal to hunt them. Some other animals are protected by international agreements (whales, elephants and gorillas, etc.)

To answer your question any better, you'd have to answer these questions first.