WHY YOU HAVE TO SAY "NO" CLEARLY
The Federal Supreme Court has ruled that as long as the police do not force an individual to do something, the individual is acting voluntarily, even if a normal person would feel very intimidated and would not reasonably feel they could say no. (see Florida v. Bostick, 1991) If you do what a policeman tells you to do before you are arrested, you are 'voluntarily' complying with their 'requests'.
Unfortunately police will often try to push citizens to accept a search, to the point of ignoring when you say "no". Its important to say very clearly "I do not consent to a warrantless search." Or "This is a private event/home/place, you may not enter without a warrant." Don't simply answer questions about searches with a simple "yes" or "no". See this case where drug police asked a confusing question and claimed they misunderstand the answer "yes" to mean they could search (October 24, 2000. Gregg County CODE officers, defendant Dockens, judge Steger, federal court, east district Texas).
Until you say "No, I don't think I'd like to do that." you are cooperating as a peer with the law enforcement officer who is trying to make the world safer. When you say "no" to a request by a police officer, you are asserting your lawful rights as a private citizen. If the officer demands you comply, then in most cases you have little choice. Usually, however, the officer is likely to try to convince you to comply voluntarily. Until and unless you say "no" and stick to it, the police don't even need any real authority to tell you what to do.
WHAT A POLICEMAN CAN MAKE YOU DO
What a Law Enforcement Officer (LEO) can demand of a citizen depends heavily on the context of the order. Most generally, police are allowed by the courts to act as any reasonable private citizen would. They may ask questions, look through windows that they happen to be near, walk or drive in public areas, etc. Without a warrant or any suspicion of illegal activity, they are allowed to interact with other citizens, but they have a limited amount of authority to demand compliance, search, or detain people or things.
In highly volatile or dangerous situations, a LEO's authority to require compliance is much higher than in non-threatening contexts. The Supreme Court has ruled (with Terry v. Ohio being one of the primary cases) that the police are allowed to protect themselves from potentially dangerous people or situations. Under the umbrella of "concern for safety" or "search for weapons" the police have wide lattitude to do what they want and to order citizens to comply with their demands.
The Terry v. Ohio case created the "weapons search", "terry search", or "terry pat" exception to the 4th Amendment 'probable cause requirement' for searches. The court ruled that if a police officer "[has] reasonable cause to believe that [someone] might be armed" they can require they submit to a quick patdown. What this has meant is that it is now standard practice to pat down anyone that a LEO wants to, without the need for arrest, probable cause, or even suspicion of a crime.
Many police use weapons pats as a way to intimidate and harass citizens, since it is a power the courts have allowed them to use with little justification. Often a LEO will find something during their patdown which is clearly not a weapon which they would like to see, but this is beyond their Court-approved authority ( see below ).
Also under the 'concern for safety' umbrella, police are given wide latitude by courts to ask individuals to comply with simple non-intrusive commands such as "stand over there" or "wait here for a moment", but the line between order and request becomes very fuzzy when an officer starts telling people where to go unless the situation is volatile / dangerous. There are many stories of two (or more) individuals confronted by police ( one example ) whom the police intentionally separate to try to intimidate or to compare stories. This is generally a 'fishing' maneuver which would not fall under the 'concern for safety' umbrella. ( see below )
During a stop for a traffic violation, police have the power to demand a proper driver's license and other state-required documentation (registration, insurance). In most [ed-all?] states they also have the power to demand sobriety tests [ed - do they need reasonable suspicion of intoxication ?]. The courts have also given police the power to frisk a driver based on the Terry v. Ohio decision (the police should have some reason to think there is danger) and some decisions have even allowed an officer (with no suspicion or cause) to search the area around the driver's seat. [ed-citation for this?]
When a private, law abiding citizen encounters police, the amount of intrusion a Law Enforcement Officer is allowed to demand is limited. Some areas have laws against "disobeying a police officer" or "obstructing an officer from their duties", but the bounds of what officers can reasonably require someone not suspected of any other criminal activity in a peaceful situation have not been clearly drawn by the courts. If someone interferes with a police officer engaged in an arrest or investigation, police tend to have very little patience and will quickly threaten or affect detainment or arrest. Generally, courts give police wide latitude in executing their duties and disobeying a "reasonable" direct order from an officer could be prosecuted in most jurisdictions.
As an encounter proceeds, the police gather data that they can use to formulate 'reasonable, articulable suspicion' or (stronger) 'probable cause' that the individual has contraband or is involved in a crime. As the level of suspicion rises, so does the LEO's authority to intrude into a person's affairs. Once the level rises to 'probable cause' to believe that there is contraband in a vehicle, the Supreme Court has made some very disturbing decisions allowing the police broad power to search in certain cases, including the power to search closed containers without a warrant. (see United States v. Ross, 456 U.S. 798 (1982) )
In a recent decision (Wyoming v. Houghton, April 1999), the Supreme Court ruled that even passengers' belongings, if left in the car, may be searched thoroughly if the driver is suspected of a crime.
In most states, you are not required to identify yourself or show the police your ID (unless you are in a vehicle). We have been unable to confirm that in Nevada that police try to charge people with obstruction of justice for people who refuse to identify themselves to police. However, if you choose to identify yourself, you are required to tell the truth. It is a crime to lie to federal police agents and it is a crime to give false identification to police in many areas [ed- find a cite for this?].
The Supreme Court has said: "A brief stop of a suspicious individual, in order to determine his identity or to maintain the status quo momentarily while obtaining more information, may be most reasonable in light of the facts known to the officer at the time." Adams v. Williams, 407 U.S. 143, 146 (1972).
If you want to avoid long and unpleasant interactions with police, do not give them any reasons to suspect you of criminal activity. Courteously decline to participate in 'fishing expiditions' or any other actions you do not wish to perform.
Police may search you 'incident to arrest': after or while arresting someone, police are allowed to search the body of the person being arrested. Recent decisions by the Supreme Court have also allowed the police to do exhaustive searches of any vehicle the arrestee was in and any containers therein. The Supreme Court held "that the police may examine the contents of any open or closed container found within the passenger compartment, 'for if the passenger compartment is within the reach of the arrestee, so will containers in it be within his reach.'" 453 U.S., at 460 (footnote omitted). See also Michigan v. Summers, 452 U.S. 692, 702 (1981).
In Pennsylvania v. Mimms, 434 U.S. 106 (1977), the Supreme Court "held that police Officers may order persons out of [463 U.S. 1032, 1048] an automobile during a stop for a traffic violation, and may frisk those persons for weapons if there is a reasonable belief that they are armed and dangerous."