I’ve been wanting to write a commentary on this subject for some time now, but these videos do a better job than I would.
Bottom line: If the police want to talk to you, whether you are innocent or not you should absolutely, positively without exception shut the hell up. Sorry to be crude about it, but the Founding Fathers gave us the 5th Amendment for a reason and there is no way–NO WAY–in which talking with the police is good idea.
[Corollary: If the IRS wants to talk with you, you want to do so only if they are giving you immunity.]
These videos run a bit long, but they are well-worth your time. (Props to Dave for the link.)