The organizations below specifically help with animal rescue efforts in the affected areas:
World Vets is a non-government organization (NGO) providing veterinary care around the globe in collaboration with animal advocacy groups, foreign governments, US and foreign military groups and veterinary professionals abroad. They are getting supplies and a first responder team ready to deploy to Japan.
The American Humane Association’s Red Star Animal Emergency Services Team is monitoring the situation closely and is reaching out to its international partners to provide a joint response to this global emergency.
The National Disaster Search Dog Foundation has deployed search and rescue teams to Japan.
The Animal Refuge Kansai is an organization in Kansai, Japan, that is preparing for a huge influx of animals from the disaster areas.
Japan’s Cat Island.
“Cat Island,” officially known as “Tashiro Island” (田代島), is an island near Ishinomaki City in Miyagi Prefecture, and it's an island for cats! Check out this Google Maps satellite view of the island.
There are approximately 100 residents on Cat Island, and most of them are over 70. One person is 37, and everybody else is over 60 years old.
So far there doesn't seem to be any news about how the Island has fared during the tsunami.
Here is a map of Japan with the area of "Cat Island" circled. Unfortunately, it is very close to the epicenter of the earthquake.