http://i.cdn.turner.com/cnn/.element/apps/cvp/3.0/swf/cnn_416x234_embed.swf?context=embed_edition&videoId=world/2011/04/13/ac.japan.quake.dogs.cnn
I think this video answers a lot of questions about the animals left behind and gives the cold hard truth about why some will never be able to come out. It is true that most animals that have been rescued from the area have not been found to have worrisome levels of radiation and so have passed inspection. There have now been 2 confirmed cases where dogs will have to be evaluated and observed because they were found to have high levels of radiation inside of their bodies. The two dogs were from deep within the exclusion zone very close to the Nuclear Power Plant. We also know that farm animals from inside the Exclusion Zone are not being accepted at the slaughterhouses to be used as food and while some horses can be saved not all of them will be. It is left to the farmers that went back into the Exclusion Zone to look after their animals to make the decision that when the food is gone to end the suffering of their animals themselves.
Regarding animals near the Fukashima plant, there is a big difference between being irradiated and being radioactive. A physics lesson follows.
How contaminated a an animal is, whether it presents a danger to others, can be readily determined with a geiger counter and 5 minutes effort.
For companion animals, whether they are a danger to others depends on how much long lived radioactive material they have absorbed into their body, not how much radioactive material they have been exposed to.
You can't eat the food animals from the exclusion zone, because they may have infections. Being irradiated will have hurt their immune systems.
But very few, if any, companion animals and working animals are contaminated enough to warrant destruction.
Also, with proper clothing and procedures, human visitors can approach the very gates of the Fukashima plant. The critical thing for your own health is not to drink ground water or food in the area, because your own health depends on minimizing radiation exposure. That is, your own health depends on both not being irradiated and not becoming radioactive by consuming radioactive materials.
But whether something or someone from the exclusion zone is a hazard to others depends on how radioactive it is, not on whether it was irradiated (exposed to radiation).
Think of irradiated potatoes and other long-life packaged products where lethal doses of radiation are used to sterilize them. They are perfectly safe to eat and in most countries don't even require special labeling. It is because they are exposed to radiation, but are not contaminated by absorbing radioactive materials.