They can pull you over for all sorts of reasons. Here are some of the biggest ones...

1. The Court of Appeals (the highest Court in NY) has decided that the stop of a vehicle is lawful when an officer has probable cause to believe that an individual has violated the Vehicle and Traffic Law. People v. Robinson (decided in 2001).  

What's definition of "Probable Cause" : "reasonable cause to believe that a person has committed an offense exists when evidence or information which appears reliable discloses facts or circumstances which are collectively of such weight and persuasiveness as to convince a person of ordinary intelligence, judgment, and experience that it is reasonably likely that such offense was committed and that such person committed it." CPL s. 70.10(2). See also People v. Russell (2005), CPL s. 140.10

That's a MOUTHFUL. So, what's that mean?  

Basically, if an officer SEES you commit any traffic infraction (from not using a turn signal, to going out of your lane, to speeding) then they have the necessary PROBABLE CAUSE to stop your car. *This is the case for most DWI stops.*

[If they pull you over for an Equipment Violation (like a tail light out or a noisy muffler) it can be a little more difficult to prove probable cause because the equipment violation may be harder to discover.]

This still counts as a good stop even if they're really after you for something else...like drunk driving.  

2. An officer may stop a car if a PASSENGER in the car was just seen driving a different car and committed a traffic violation. People v. Sluszka (2005) [seeing you change cars is considered like a continuation of your initial driving.

3. They can stop you if they have reasonable suspicion of criminal activity (i.e. a misdemeanor or a felony). Reasonable suspicion is: "the quantum of knowledge sufficient to induce an ordinarily prudent and cautious man under the circumstances to believe that criminal activity is at hand." People v. Cantor (1975)

The police just need to say that they saw something that led them to believe that "criminal activity is at hand." They need facts.

Original article: http://www.ithacadwi.com/when-does-a-police-officer-have-the-right-to-pull-you-over-in-new-york