The movie OUTBREAK is the one I think of. Cute lil monkey, smuggled in is carrier of Ebola Virus- spits on guy that smuggled him in. Contagion spreads.
Dustin Hoffman saves the day just as the Government gets ready to set off a fuel air bomb to kill everyone, even though they found the monkey and developed a cure.
The town was quarantined, and the evil guy in authority wanted to keep the cure so that the government would have a perfect bio weapon.
Andromeda Strain could be added to the list.