In Lane county there is no restrictions on cats although if your cat does get picked up, they will make you pay an impound fee! I didn't know this. Im not seeing anything about restrictions on how many dogs a person can have although they do have a section on kennel licences so I figure there HAS to be some sort of limit.
In Carson City the maximum ammount in the city limits was 3 dogs. No limit on cats there either unless there was evidence of abuse or neglect.