The proper name of those beaver statues?

What are those beaver (beaver) statues called traditionally put in front of stores for luck but have been replaced in large by that cat with the waving paw?

They are not beavers. Neither have they been replaced by cats. I assume you are referring to tanuki statues:
http://en.wikipedia.org/wiki/Tanuki

Obviously you have never seen a beaver..they have big teeth in front, a different fur...a different tail (more like a paddle..) and webbed feet
http://en.wikipedia.org/wiki/File:American_Beaver.jpg

compare it to a raccoon dog (Tanuki) from Japan:
http://en.wikipedia.org/wiki/File:Tanuki01_960.jpg

about the ones in front of restaurants:
http://www.onmarkproductions.com/html/tanuki.shtml

Tanuki is brilliant! You only see him at restaurants, and as the link above says, his hat, bag of coins, notebook, bottle of sake, and big testes all have particular relevence. I bought a reasonable size one back with me on one trip, and on subsequent trips I have bought back a frog and an owl to keep him company. I've seen them in a zoo as well, but there arent quite as attractive in the flesh.