Why do dogs come in all shapes, but cats are generally all the same?
Until recently, cats were not extensively selectively bred, but were allowed to roam freely and therefore interbred randomly.  Darwin pointed this out, contrasting cats to species that were routinely "enclosed":


  On the other hand, cats, from their nocturnal rambling habits, can not be easily matched, and, although so much valued by women and children, we rarely see a distinct breed long kept up; such breeds as we do sometimes see are almost always imported from some other country.


In contrast, dogs and some other species were selectively bred for certain characteristics "each good for man in different ways":


  The key is man's power of accumulative selection: nature gives successive variations; man adds them up in certain directions useful to him. In this sense he may be said to have made for himself useful breeds.


Why were cats not selectively bred, while dogs were? This gets to be somewhat speculative, but it's clear from looking at dog breeds that many of the different breed functions need to have a larger animal than a cat, as well as one with different personality: Herding sheep, hunting foxes or badgers, fighting bulls, etc.  Cats' function for humans has traditionally been to hunt mice and rats, a role for which they're already beautifully adapted.  

(There are a number of small dog breeds, of course, but these parallel cat breeds in that many are ornamental, or else originated as rat-hunters.)