Under what circumstances can the police stop me while driving?
They're supposed to only stop you if they believe some type of offense has been committed or they have a suspicion of such an offense. However, under most State vehicle codes there are so many offenses that almost anything you can think of doing could be an offense. Anything from a dome light out in your car, to a cracked taillight, even minor things, if they think your tires are bald, any minor offense, they have the right to stop you and then question you.