If you are stopped by the police are you required to answer questions, provide identification, even give them your name? The answer to all of those questions is no (in some states, the answer to the last question is possibly yes, however if giving your name could be a violation of the 5^th Ammendment then, it's probably still no — in any event, very few states have laws to this effect).
I have been in more than one situation where I was stopped by the police, and many where I was put in a position where I might be. One of the most important things to remember when you are even just stopped by the police is to not break any more laws. If you are stopped by the police and you run or physically resist arrest these are both crimes, even if the original arrest is deemed unlawful.
If you have ever watched an episode of Law & Order you know, police will lie to get you to to achieve their means. If this means telling you that they could easily get a search warrant, but it's "better" if you cooperate this most likely means the exact opposite. If the police had probable cause they would be able to get a search warrant they would *get* one and come bang down your door in force, not politely ask for your permission to enter.
If a police officer stops you on the street, there are two, and only two questions you should ask.

• Am I under arrest?
• Am I free to go?

Be forceful if you need to in getting direct answers to these questions. Under virtually all circumstances if the answer to the first question is no, the answer to the 2nd is yes.
If a police officer comes to your home step outside and close the door behind you. If they ask for a glass of water suggest to them the location of the nearest vending machine (I'm in suburban NJ so there is a small store 2 blocks left and 4 blocks up the hill). If they ask to use the restroom, tell them the location of the neareset restroom. Once you have invited a police officer into your home you provide them with an opportunity to poke around. The laws on this are somewhat vague, however rifling through the garbage in the bathroom after invited into the house would not be a violation of your 4^th Ammendment rights, however opening a medicine cabinet and reading your prescriptions would be… however if that same medicine cabinet is already open, reading those prescription bottles would not be a violation.
How I got onto this track and writing this entry is also rather fascinating. Have you ever gone to a retail store such as BestBuy where, upon leaving they insist that you show them your recipt and verify the contents of your packages? I have, and have been mildly put-off by it on many occasions. For one thing, I dislike having yet another person go through my paid-for items looking at what I bought. I also dislike what is the accusation that I am a thief. And, make no mistake, that is what they are saying by their loss-prevention policies is that they believe that every customer is a thief and as such every customer is compelled to be checked by law.
This, however, is a rather large misnomer.
Once you have paid for these items they are yours and as such you have the right to leave the store without submitting to any such searches of your person or personal belongings (which, since you have paid for them, the items in your bag/cart are now). Exit bag checks are strictly voluntary.
If you are requested by a store employee to check your recipt a simple "no, thank you" is a sufficent response.
The exact legality of it is discussed here:

Are Door Bag Searches Legal?

Yes, as long as the inspection is voluntary. No, if the bag check is involuntary or coerced. This is a rather fine legal distinction that is subject to misunderstanding and abuse. Basically, nothing in the law gives the merchant the right to detain a customer for the purpose of searching a shopping bag unless there is a reasonable suspicion of retail theft.

In fact, as the article goes on to explain, store employees and "security guards" have very little power, they are not officers of the law and have only one single option which is to make a citizens arrest and await the arrival of police to preform a search if the person does not consent to one. Only the police can preform an involuntary search based on probable cause. Store employees must satisfy the following conditions before satisfying a claim of probable cause.

1. You must see the shoplifter approach your merchandise

You must see the shoplifter select your merchandise

2. You must see the shoplifter conceal or carry away or convert your merchandise
3. You must maintain continuous observation the shoplifter
4. You must see the shoplifter fail to pay for the merchandise
5. You must approach the shoplifter outside of the store

This is discussed in more detail here.
I intend to try this out the next time I am confronted at a retail outlet.
Simply, this is not an easy burden to meet, but store merchants rely upon the ignorance of the average shopper just like the police rely on the ignorance of the average person to serve their needs. If you don't know what your rights are then you won't be exercising them any time soon.
I have been asked many times, by many people why, if I am a law-abiding citizen, that I should even be concerned with any of the above, if i'm not breaking any laws then I have nothing to hide, right? This is simply not true. Opressive regiemes such as the one that the USA is currently hosting in office have, can and will continue to exercise their power beyond the boundries of the law to quell resistance.
They did it before and they are doing it again.
The article that got me started on this which I found via Boing Boing.
ACLU Bust Card Memorize this, it explains exactly what to do and what not to do in the event you are detained by the police, knowing that they will lie to you to coerece information from you it is invaluble knowing exactly what you is illegal for you to do.
The Vaults of Erowid another site I came across while writing this entry, very interesting.