It has not (yet) reached the point where the police can stop the operator of a motor vehicle for no reason whatsoever. You are protected from “unreasonable searches and seizures“. Judges decide where to draw the line between reasonable and unreasonable searches and seizures.
When you are in your house, the police are generally required to have more evidence before they can search your property and seize (arrest) you. In a motor vehicle, you enjoy a lower level of protection from unreasonable searches and seizures.
The police cannot stop a citizen just because “you look suspicious”. Courts have held that the police must have specific and articulable facts which, taken together with rational inferences from those facts, reasonably warrant the intrusion that a stop involves. These are known as invesitgatory stops.
If the police directly observe you committing a traffic violation, such as speeding, they are entitled to stop you for a brief enough period to investigate the traffic violation. That is where your troubles can start.
Once they do stop you for a routine traffic offense, they may then further their investigation if they believe you may be driving under the influence of alcohol. Common signs are an odor of alcohol, bloodshot eyes, slurred speech, open containers in the vehicle and difficulty locating your driver’s license, registration or insurance card.
The police are also entitled to investigate if they find you pulled over to the side of the road, or asleep in your vehicle or after you have been involved in an accident, even if the accident was not your fault. They are also, under proper circumstances, permitted to erect DUI roadblocks.
It can be more complicated when the police do not actually observe you committing an offense but have reason to believe that you may have. A citizen’s complaint, from someone whom the police have reasonable grounds to believe is reliable, will justify a stop.