Albuquerque has historically allowed chickens and I'm not sure what else. I know in the unincorporated areas of the county (some of which are fairly urbanized) cows, sheep, goats and horses are common. We are not a particularly dense city, so nuisance issues are perhaps not as big as in other places.
If you go to this site:
http://urbanchickens.org/ you can access a listing of municipalities that allow the keeping of chickens. The organization is run out of Albuquerque where this is an increasingly popular thing.
As for the noise of roosters, most places do restrict them (here you can only have one, if I recall correctly), but as the director of the above organization told me recently, if there are no roosters, hens will often take on the rooster role, including crowing. Who knew?
The popularity of chickens is, I think, directly related to an increased interest in local food production and the recession. We have seen a very big interest in gardening, including community gardens, here. I think people view producing some of their own food as a tangible way to impact their household budget.