For me, animals don't pose danger, people do!  In other words, the relatively few times I've felt worried about my own safety because of an animal, it's been because of what we (humans) are up to.   

My scariest moment was during a trip to Nepal when I worked as a scientific advisor for Discovery on a filming project.  We'd flown by helicopter to an isolated part of the Makalu-Barun forest, a large protected area near Mount Everest.  I had joined a team led by Conservation International to survey the region's wildlife in coordination with a visit by Jeff Corwin who was making a TV film about the search for the yeti.  (See link below.)

Alot of work had been done to secure permits and permissions for the team's presence, but not enough, as it turned out.  When nearby Maoist rebels found a group of scientists surveying plants, they pulled out guns and insisted on being paid thousands of dollars for access to the forest, threatening to shoot down the next helicopter.  That meant Jeff's copter.  We could cancel his visit, of course.  But how were we going to leave?  The negotiations were tense and money was paid.  The rebels seemed particularly upset that the scientific team included Nepalese who worked for government universities.  

If you've followed any of the news in Nepal since that time (2005), the Maoists have gained more and more power in the government.  That was scary, and way more dangerous than what subsequently turned out to be a difficult three weeks that included camping at 4400 meters in an icy snow storm. At the end of the trip, I found myself at the Kathmandu Zoo taking care of a sick sloth bear, a species Jeff considered in the running for the yeti.

The outcome of it all was Corwins's Quest: Realm of the Yeti