The most common cause is when a guest ends up in an exhibit. This usually happens when you have a boardwalk overhead of an exhibit (which for some reason causes guests to fall off and down into the exhibit). It will NEVER occur to the guest that THEY have fallen into the exhibit, they will instead seriously believe that whatever they are in with has escaped. As a result, other guests also then believe the animal or animals have escaped, even though it safetly contained in it's exhibit and they are not in with it.
Another time this is likely to happen is when the density of people around an enclosure increases (and therefore the chance of one of them ending up in the exhibit increases). For some reason, this problem occurs most frequently with Ethiopian wolves. One of the females gives birth, half the zoo come to see them and somebody ends up in with them. Occasionally, the wolves seem to take an objection to the large crowds and even if there is nobody in with them, start to stalk people through the perimeter fence. This also causes the guests to panic for no apparent reason.
There are two solutions:
1) Remove boardwalks where guests are frequently falling off
2) Fence off an exhibit around the time an animal has just given birth. From memory, Ethiopian wolves are only pups for around 4-6 Zoo Tycoon 2 weeks so if you fence off the exhibit for the first 3 weeks, then by the time it's open for viewing, the pups will only be a couple of weeks away from becoming adults (adults don't generate the same insane level of interest). I either do this, or make the Ethiopian Wolf exhibit only viewable by a Zoo Tour to ensure their privacy and prevent this issue.