Most of us are raised to believe that the police are here to protect us and that we should cooperate with them whenever we can. For the most part, that is true; they are and we should. But, when your reputation and integrity and freedom are on the line, there are limits. In fact, those limits are so important to American culture that they are part of the Constitution.
Police Officers with their uniforms and guns and badges and red lights and moustaches can be very intimidating. In fact, they are trained to be intimidating. They are trained to make you feel powerless against them. When they are dealing with real bad guys, that is a good thing. When they are dealing with you, the regular person who has never had a run-in with the law, it makes them look like a*holes and it makes you feel weak. But, you are NOT weak.
Information like your name, address, and date of birth is not, by itself, incriminating and not generally protected by the Fifth Amendment. On the other hand, questions about where you have been, where you are going, and what are you doing are generally protected and up to you to answer or not. If you choose not to answer, you will not probably be breaking any laws. Of course, while your rights may be preserved, you will have one frustrated and pissed-off cop. It has been my experience that the more frustrated and pissed-off the cop, the less of a sense of humor he or she will have. But, then again, freedom isn't free.
When a law enforcement officer asks something like, "where are you going?" and you respectfully and politely answer with something like, "that's not really any of your concern," which you are entitled to do, you will immediately see the officer's face turn red and you may even see smoke emitting from the ears. Then, as they say, "it's on." Using tone and vocabulary and calculated body language, they will attempt to intimidate you into giving them what they want. They may even say things like, "...how 'bout I take you to jail and let you think about your answer there?" or "...do you WANT me to give you a ticket?" The fact is, if they CAN take you to jail or give you a ticket, they are going to; you have no obligation whatsoever to make their case against you any easier. So, don't say anything. And if they do arrest you, say politely, "I want an attorney present during any questioning." Once you say that, they are PROHIBITED from asking any questions about the case for which you have been arrested.
Even then they will use passive-aggressive techniques to get you to talk. They may tell their partner something like, "...we don't really want this guy, but he won't help himself..." or "...he wants his lawyer, so don't ask him any questions...even though he would probably get out tonight if he just helped us." Stay strong. Stay quiet. Don't let them manipulate you. Whatever they say, their ultimate goal is to build their case against YOU.
"...but if I have nothing to hide, then I have nothing to worry about." Really? Is that how so many innocent people with nothing to hide get convicted by their own statements? If you have nothing to hide, that's great. Let your lawyer explain that you have nothing to hide. Law enforcement is trained to ask leading and misleading questions, to provide you the paint with which to paint yourself into a corner. Just remain silent.
When you come home and find the detective's business card on your door with a note saying they "need your help" with an investigation, call a Criminal Defense Lawyer first. Even if you are sure it has nothing to do with you. You never know what somebody said about you behind your back. You can still help with the investigation, you can still be a good guy. Just protect yourself at the same time. Bring a lawyer with you.
Finally, remaining silent means remain silent. Your cellmates are not your friends. Your friends are not your friends. When you are in custody, you have no friends. So do not talk about your case with ANYONE! Wait for your lawyer.