Well, what about that enigmatic red cat with the raised paw that is so ubiquitous throughout Japan? It seems like every secretary, every shopkeeper, has one on their desk. What's up with that?
When I was researching Japanese history for purposes which need not concern us here, I read that way back in the Yayoi Era (300 B.C. – A.D. 300) an emperor was traveling through the countryside on horseback. Suddenly it began to rain. He looked over at a house he was passing and noticed a cat sitting on the porch; when he met its eye it waved at him. Intrigued, he dismounted and approached, while behind him, his horse was killed by a lightning bolt. The grateful emporer declared that henceforth the cat would be memorialized for saving his life. That's why this waving cat is a symbol of good luck.
Sorry, I can't remember where I read this bit of lore.
jinmyo alerted me to the fact that there's another version of this story at Maneki Neko, and I see there's also one at The beckoning cat. Interesting that they're all a little different, though.