My late Father, who dropped out of high school to work in the 1930's - provided some wisdom on this topic that I'll share with you.
He used to say that nobody ever got hanged for something he didn't say.
Until this week, that was pretty good advice. But now it needs a bit of updating.
Nobody ever got hanged for invoking the Fifth.
Remember when Tony and Big Pussy executed that Belocqua kid, the one who'd shot Christopher? And the FBI came to Tony's house and asked him to get down to their office? Next scene, Tony's talking with his crusty old veteran lawyer. He says that if the G had a case, this conversation would be taking place through glass. Tony asks why they want him to make a statement. The lawyer tells Tony - astutely - that they want to pin him down to a story. Any story. So that if he changes it at trial, they can make him look like a liar. It should be added that it will enable them to better obtain and prepare evidence to refute any alibi. An alibi normally is one of the few things that a defendant must give notice of to the prosecution before trial, but the earlier the FBI knows about it, the better they can try to puncture it.
I want to add something else to the mix. This is important. Whenever you tell LE anything, you create a dangerous risk. That risk is that the agent/officer/detective is then open to write whatever he wants in his notebook. There just may be an honest failure to communicate and he may innocently write down something different from what you said. Or he can set you up by deliberately writing something else in his notes. It is a crime to lie to a cop in every jurisdiction. Pressure may be exerted upon you to testify to what's in that notebook if you are a witness, even if it is not what you believe that you said, even if you believe it to be untrue, by the threat of a prosecution for lying when interviewed. And if you are the target, anything you say is admissible if it is voluntary, etc. You avoid all this risk by saying nothing. I did some writing about all of this thirteen years ago and it's still good advice:
http://www.xxxlaw.com/articles/if-you-get-arrested.html