www.catster.com lists the top ten cat breeds in the USA. There are a lot of websites that do this including mine. I say that the methods used by www.catster.com and others is at least potentially flawed. I'll tell you why. They base popularity on the number of registrations of purebred cats with the Cat Fanciers Association (CFA). The CFA is probably the world's largest and most prestigious cat association. They are quite conservative and have fostered the breeding of the flat-faced Persian, an inherently unhealthy purebred cat because it is bred to extreme.
Basing popularity of a cat breed, with the public, on the number of cats that a cat breeder registers with the CFA might reflect public opinion but it might not. All it does for certain is count the number of registered cats. There might be public demand for these cat breeds. On the other hand the cats might be given away to friends, for all we know.
There is no automatic connection between simple registration of a purebred cat and its popularity with the public. The only way to ascertain public opinion is in a large poll. PoC has a large poll of almost 4,500 votes at Dec 2011 and the top spot by a clear margin is the Maine Coon. The Persian has dropped back in recent years to 6th spot. See the top 10 cat breeds.