I've heard that lions and tigers aren't actually that dangerous. Some big cats have a very vicious fear response, but lions and tigers are apex predators, and no one in their natural environment can really fuck with them, so they've lost that kind of behavior. The only real risk with lions and tigers is if they get hungry, or if you try and play with them, because they don't really realize how strong they are.

I'm not going to test this theory myself, but here's a cute story about a lion who was raised by humans and still recognized them even after being reintroduced into the wild: http://en.wikipedia.org/wiki/Christian_the_lion