Schneier on Security: Why You Should Never Talk to the PoliceIt's very persuasive. In particular, there's a funny kink in American law. Whereas "anything you say may be used against you", the converse is not true; exculpatory statements are inadmissible hearsay.
This is an engaging and fascinating video presentation by Professor James Duane of the Regent University School of Law, explaining why -- in a criminal matter -- you should never, ever, ever talk to the police or any other government agent. It doesn't matter if you're guilty or innocent, if you have an alibi or not -- it isn't possible for anything you say to help you, and it's very possible that innocuous things you say will hurt you.
The other lesson that stuck with me is that non-videotaped statements are very prone to being remembered differently by different people. These are the majority of statements made to police.
In comments there's a reference to an ACLU guideline for persons stopped by police. Two of the frequently repeated items are "don't say anything without a lawyer" and "be clear you do not consent to search".
In practice I'll speak with police if I think I can help with law enforcement -- though that's rarely come up in my life. Most of my non-casual conversations with police ended when I bought a car with cruise control.