Arturo asks, "A few years ago, during a loud party at our house, our not-so-friendly neighbor called the cops. When the police arrived, they told us to shut the music off and be considerate towards the neighbors. I was not arrested or fingerprinted or taken to the police station, but the cop left me with an incident report card. Do I need to mention this on my application for US citizenship?"
As you say, since you were not arrested nor did you ever face a judge, it was not a crime that you committed in the eyes of the law. It was merely an interaction with a law enforcement agent that need not be reported for the purpose of naturalization (for instance, simply because you were stopped by a traffic cop for a broken light and then let go with a friendly advice to fix it, it is almost if the incident never happened because it will not be on your record). Conclusion: no need to include it because it will not show up in a background check and will only confuse the agents. Needless to add that if this comes up during the interview, since you will be under oath, you will have to provide the details.