I have no idea if the city has a limit. I've been told by word of mouth it is around the 3 dog mark, but have yet to see proof of this.
Most rental places have a max of two dogs. And I honestly think the regulations regarding pets may be up to the individual neighborhood/etc. For example, out where my parents live, there isn't a dog/cat limit, but if you want to have livestock you have to make sure all of your nearby neighbors are okay with what you're getting/how many you're getting.
Where Mike and I are at now doesn't care about pets/breed/etc, as long as you clean up after them, they aren't destroying the landscape, you keep them contained, and you don't have any noise complaints. We have Cynder and Abrams (and before had Cynder, Gracie, and Cooper), and a neighbor has three big dogs. The landlord actually has four dogs, one of which is a Pittie. So very dog friendly out here.
We are supposed to license the dog with the city...have never done that, and I don't think many people do. LOL