I've noticed a large number of US TV shows (many of which involve the police) constantly feature people instantly and without hesitation assisting the police in their enquiries. I don't want to say it's brainwashing, but it's not far off.
Let's say you decide to talk with them. Now that you are talking to them, if they decide during that conversation that you've "become agitated" and pull out their gun and shoot you in their "self defense", guess who investigates them? That's right, the FBI.
Guess how many times in the history of the FBI an officer was found to have shot someone inappropriately, even if they weren't armed? That's right, zero times.
FBI knocking on your door wouldn't be one of them though. At least for me, but to each his own.
manish_gill's linked video is an amazing example of the information/power asymmetry working against you in this game. By the time you realize you're in an "uncomfortable place", it's likely too late.
Say nothing, ever, for any reason. [0]
The only thing you should ever say to Police is, "Am I suspected of committing a crime?"
if (crime_suspect) {
lawyer(yourself);
} else {
print "Thank you, have a nice day.";
}
Assuming instantly pleading the Fifth helps misses the bit where police and especially more powerful organizations like the FBI jump to and act on a lot of conclusions that aren't admissible in court (and of course have plenty of capability to find non-verbal, admissible evidence of wrongdoing if motivated to look for it, even if you're innocent). If they're casually following up a dubious lead, which they probably are if you're not expecting their visit and don't have pot plants or a server mirroring Wikileaks in your conservatory, you probably don't want to fit their mental model of a suspect, which probably means you being at least slightly curious about why they want to speak to you, and at least willing to entertain the possibility that you're not the suspect. Statistically, you're more likely to plead the Fifth if you're guilty.
(This probably doesn't apply when they're picking on you because you're a genuine suspect or there are political reasons for them trying to find out about your friends or organization.)
It's more along the lines of: if a friendly law enforcement officer comes up to you and politely asks you some questions, many people have no problem being polite in return and answering them. Often the officer(s) will say something like "I just want to ask a few things, then I'll leave."
So 1) you'll think that the more you cooperate, the sooner you will be free from their presence, 2) you may fear that if you don't cooperate at all, they may harass you more, and finally 3) they may act like they are "doing you a favor" and so you may feel a bit compelled to do them a favor in return.
Federal agents in particular (FBI etc.) typically go this route. They'll try to build a rapport, "you-help-me, I-help-you", and may or may not subtly imply that if you don't respond they'll return for further questioning. They may even use classic interrogation tactics to make you more likely to answer them.
By simply not being accusatory or impolite, they have a much greater chance of getting the information they want.
If a cop or FBI agent is seeking to talk to you, specifically by looking for you in the first place, you have far bigger problems than you can possibly talk your way out of, regardless of how innocent you actually are.
If the FBI have opened a file on there you probably don't want the words "suspicious of law enforcement" added to the list.
The police are hoping you lie, because now they can easily trip you up later in court. Often they will just nod their heads and accept your complete BS and write it all down to give to the prosecutor. They will listen to an hour's worth of fabrications and pretend to be fooled by it so you talk some more, then arrest you because now you have provided them all they need.
In the UK police do this all the time with suspected drug importers. They show up and claim to whoever answers the door that if they tell them where the drugs are, this will all be sorted out with a fine or something and they will be on their way. The fool at the door agrees and now their entire place is ripped apart by a search and they are arrested and charged. There is a fine in UK/Ireland for cannabis drug posession, not for importing though.