Working under the assumption that 99% of people can't, even selectively, play the game and win, the only broad statement that anyone can responsibly make is to advise not to speak to the police without a lawyer. I've seen clear cut victims and witnesses become suspects in a heartbeat. The only thing I could imagine talking to the police about is a situation where the other person involved really needs to be arrested or hospitalized or else some great harm will come to the victim.
I saw someone (complete stranger) fall off a building once (he was alive the last time I saw him, but that's not saying much), well, I saw them impact the ground at least as I was driving by. When it happened I was already on the phone with 9-1-1 about something else so the whole thing was documented and recorded. When I was eventually interviewed, some of the detective's questions were geared towards determining whether I pushed the guy off the roof.
You don't want any involvement with a crime or potential crime if you can at all avoid it. You have to balance this with your need for the police and your sense of civic duty and justice sometimes. If you're guilty, don't talk, nothing you say can help you. Respectfully ask for a lawyer at the outset: "I would be happy to help in any way that I can, but I need to speak to my lawyer first." Every other shade of gray is a roll of the dice as to whether you come out on top or not. If the stakes are small, like a fender bender, you might be able to help yourself. If they found pot in your jacket, shut your mouth.