There are some state wiretapping laws that make it illegal to record audio of people without their consent, but the courts have consistently held that the First Amendment protects citizens' right to record the police when they're on the job. The police can't stop you unless you're interfering with their work -- and they can't take away your smart phone or delete the recordings just because you took video. Police need a warrant to mess with the content of your cell phone.
The Department of Justice has even officially weighed in on citizen recordings of law enforcement officers. Here's what it said in a 2012 letter to attorneys for the Baltimore Police Department:
Policies should affirmatively set forth the contours of individuals’ First Amendment right to observe and record police officers engaged in the public discharge of their duties. Recording governmental officers engaged in public duties is a form of speech through which private individuals may gather and disseminate information of public concern, including the conduct of law enforcement officers.
Obviously, just because you have the right doesn't mean all law enforcement officials will respect it. But there's also a growing movement to make sure that police actions are almost always facing the scrutiny of video evidence by use of mandatory body cameras, or "bodycams," on officers.
The cameras could potentially provide an extra layer of digital oversight over law enforcement behavior -- as well as a way for officers to verify their side of the story if a situation gets messy.
In the wake of the Ferguson protests, makers of such devices have seen their business boom.
Even the American Civil Liberties Union is on board with the the use of bodycams, albeit with a few caveats about data retention and privacy implications. "Although we generally take a dim view of the proliferation of surveillance cameras in American life, police on-body cameras are different because of their potential to serve as a check against the abuse of power by police officers," the group said in a 2013 policy paper.