Like Nicole, ours is incredibly quiet. We don't have one. (Dang! I was hoping I'd be the first with that joke.) Most homes in our area don't have them, because we only have a few really warm days here in summer. I'm not a huge fan of AC, so it works for me.
But, AC units are infamous for being quite loud. In the City of Seattle, HVAC units are considered "noise producers" that need a noise study before getting a permit. That may only be for commercial developments, but residential units are loud as well.
Moral of the story: Don't install a new AC unit, especially anywhere near a neighbor's property, without thoroughly considering the noise it produces.