Munchkin cats have actually grown in popularity in some cases.
I first learned about them a few years back, and even now it can be hard to find solid and NEW information on them, most of what I have come across is the same jabber over and over.
At one time they were promoted as having no defects and a lot of people wanted them, a lot still do. I happen to fancy the munchkin la pur, but not sure exactly how keen I am on the continuation of breeding them.
The common question was if they suffer from the same spinal problems dashies can and the answer was no, but often failed to mention, or were not aware of this compression defect of the heart and lungs.
While I'm not thrilled about yet another "ornamental" breed, but if they breed for health as some claim is their goal, I can not be against it in it's entirety. As it is a genetic mutation, much like polydactlism, breeding for it intentionally or not, there will still arise cases.
However, what a lot of people fail to consider when wanting to breed munchkins, is that only about 1 out of every 8 or so kittens will actually be a munchkin, so then you are left with a horde of normal cats and no one to adopt them.
While the "breed" is part of TICA I do not believe if is part of the CFA.
As for the floppy cats. *sigh*
Their other name is Twisty cats, I feel it is a horrible and needless purposefull genetic mutation this one sick minded lady happens to breed for. There is a lot of information you can find on it, but quickly, kind of picture a cross between a cat, and a rabbit.
I have heard it is basically stemmed from attempted breedings of polydactyl cats together, but I'm not sure if genetically it would actually work that way, as I believe polydactylism is a spur mutation, meaning it's something far more complex then just breeding polydactyl cats togeth and expect their offspring to be the same. It doesn't work that way.