The scientific community is divided on this topic. There is evidence for some animal behavior, such as birds flying lower before a storm. The bird's complicated and fragile respiratory system is sensitive to air pressure changes that make the bird uncomfortable. They tend to stay close to trees before storms, to stay close to shelter and to avoid air pressure discomfort. Researchers in Florida have found that sharks seek deeper water before a hurricane!
In NATURE's Can Animals Predict Disaster? a geologist in California reports an increase in missing pets before an earthquake strikes.
However, the US Geological survey asserts that you cannot predict the weather by changes in animal behavior alone. So far, no one has really been able to reproduce results in a lab.
It's possible that your furry companions can sense infrasonic sounds that we can't hear. Dogs can get spooked from thunderstorms because they can hear much more of it than we can...and it sounds much louder! Storms and earthquake produce these sounds, too.
What do YOU think? Do you or your pets have any ways of predicting bad weather?