I'm not actually aware of a specific account of it raining cats or dogs anywhere, but there have been reports of other animals falling from the sky like rain. Strange rains have been documented in different parts of the world at different points in time. Here are some examples:
- In Kansas City, Missouri in 1873, frogs fell from the sky during a storm.
- Several one foot long alligators fell on a farm in South Carolina in 1877.
- In Worcester, England in 1881, a thunderstorm rained down periwinkles and hermit crabs.
- In Naphilon, Greece in 1981, frogs also rained down from the sky during a storm. Oddly enough, it was an African species of frog!
- In Ipswich, Australia in 1989, around 800 sardines apparently fell from the sky during a light shower.
- Thousands of corn husks fell on Wichita, Kansas in 2001.
You can find more examples here.
The most recent example I have heard about is a tadpole rain in Japan that occurred earlier this year. Tadpoles mysteriously rained down around Hiroshima, Japan.
One of the most popular theories to explain some of these cases is that a waterspout or tornado may have picked up the various "strange rains" and carried them in the air where they rained down from the sky. Sometimes airplanes or birds may be implicated. Although these explanations may explain some of the cases, none of these explanations can necessarily explain all the cases. For one, if waterspouts or tornadoes are the culprits, how is it that they seem to only pick up one type of object or animal? Potentially, you'd think there be a whole mess of different things strewn about. In the Greek case that I mentioned above, the frogs weren't even native to the area either! As for airplanes, there are many cases of these strange rains occurring before airplanes were invented. Birds may have been able to pick up some of the objects and animals that have fell from the sky, but some of the animals would have probably been to heavy for most birds. It's also odd that birds would pick up so many of the same type of animal or object and then proceed to fly to a certain location and just drop them.
In addition to raining various different animals and objects, there are some cases where water rained down on one specific spot. Consider these cases from the Carolina's in 1886:
- Rained poured down on a piece of land in Chesterfield, South Carolina for 14 days. Oddly enough, there weren't even any clouds the rain could be attributed to.
- The Charlotte Chronicle in North Carolina reported that several eyewitnesses observed rain falling on one specific spot between two red oak trees at 3 PM everyday over a three week period. It was always sunny too.
- A 10 foot piece of land in Aiken, South Carolina received rainfall too.
There really doesn't seem to be a good explanation for many of these strange rains. They are very mysterious indeed.