It seems more and more that actual criminals who are on trial use it as protection.
The thing is that no one's a real criminal until they've been convicted. One of the reasons this right exists (and Canadians have it, too) is that even innocent people can give testimony that incriminates themselves. That is, they say something that can make the judge or jurors think they're guilty.
I think it was someone on here that posted the link, but anyway I remember being linked to a video of a Defense Lawyer given a lecture to law students. The freaking thing was like an hour long, but I watched it anyway. He described how talking to the cops - even when you're innocent - can be dangerous, even if everyone is on the up and up.
An example he provided went something like this: The cops are investigating a murder, and are questioning you about it; you say you were at your mother's at the time and she lives an hour away. However, the cops find a witness - a fair, impartial woman who has no reason to lie - tells the cops she saw you at a store only a couple miles away from the crime around that time. She's wrong, she mistook you for someone else, but that's what she's told the cops. Now, the cops - and the jury eventually - are gonna think you were lying about your whereabouts and suddenly they're not believing anything you've said and you're chances off getting convicted go up. Whereas if you'd said nothing to the cops, they'd still have you placed near the crime, but they wouldn't have any "evidence" that you'd been lying and wouldn't have enough to get to court.
The story went something like that, anyway. The message was "Always tell your clients to tell the cops nothing. Even if your client is innocent."