Breed bans (aka breed specific laws) can be found in quite a few juridictions. Usually they are directed against Pit Bulls (and cognate breeds) and Rottweilers. Quite a few European countries have much more comprehensive breed bans. Usually rare breeds with limited followings are singled out since there is little political liability in doing so. This amounts to a combination of meaningless "feelgood" legislation and a ceremonial witch-burning. Some countries have gone so far as to outlaw breeds that are already extinct!
In some jurisdictions, the breed bans entail outrageous violations of civil liberties: They give animal control officers the power to enter homes at will and seize any dog that in their opinion looks like a Pit Bull or might be part Pit Bull. In essences--any medium-sized smooth-haired mixed breed could be seized and destroyed (Boxer mixes, even Lab mixes would be at risk). Ironically, such legislation is particularly popular in so-called "liberal" jurisdictions like Denver, CO.
Elsewhere, many insurance companies will not issue homeowner policies to anyone who has a breed they disapprove of: Not only the usual suspects, but such seemingly innocuous breeds as Bernese Mountain Dogs and such obscure breeds as the Karelian Bear Dog and the Russo-Finnish Laika. (These are all on the Auto Club's proscribed list.)
Some dog advocates have supported "vicious dog laws" as an alternative to breed specific laws. Unfortunately, many of these are written so that any spirited dog (e.g., one that chases a cat) could be classified as a "vicious dog."