I have to agree with Jared. As someone who has spent the last 15 years in apartments (or dorms, for that matter, as I did when I got my first budgie in '93), I've always had to take noise levels into consideration.
Don't misunderstand me: I like parrots of all sizes and noise levels. I'm feel the same way about dogs and for the most part, children

That said, I do not think that a screaming 'too, a shrieking child or a howling dog is something that anyone should be subjected to for hours and hours and hours. We all know that parrots will be noisy when they want to be and dogs are much the shame. Sure, a person has a right to have a parrot or a dog but you do not have a right to subject a neighbor to the noise.
In areas where neighbors are in close proximity to each other it stands to reason that people are going to be sensitive to noise levels. There will always be a nitpicky neighbor in some neighborhoods; the type of person who doesn't like someone for no good reason at all. But there are noise complaints that are legitimate complaints.
Everyone has a right to live peaceably. I would hope that in the case of noisy pets or children (or for that matter, adults and vehicles), neighbors could try to work things out on their own before involving the municipality or the local law enforcement agency.