I've lived in three major cities (East Coast, Midwest and West Coast) over the last 15+ years, and I've found that the response depends a lot on the city and what you are calling about.
- Most recently, a young woman showed up randomly at our door, claiming people were following her and that she was scared (she was probably mentally ill). We called 911, and cops were there in less than 5 minutes.
- We've had various instances of bad behavior at the local park, such as doing drugs, which I've reported on the non-emergency line. To my knowledge, no one ever showed up.
- When I was in Big Midwest City, I once had the cops and fire department banging on my door, claiming someone had called 911 from my apartment. My apartment number was something like D309, and their dispatch instructions only said apartment D30, which would have been every apartment on my floor. Ooops! Of course, they did not believe me and wanted to "inspect my apartment." I politely told them no.
- In various places, I've called to complain about loud neighbors (non-emergency only). The only time I remember a response was when I heard someone threatening someone else.