Know your rights.
If you live in the United States you have a constitutional right to photograph plainly visible public spaces. This includes police and government workers carrying out their duties so long as you are not interfering in them. Unfortunately there have been many instances where police officers get aggressive in the faces of cameras.
Keep in mind that some states regulate audio under wiretapping laws (and since videos contain audio, it is treated differently than if you were to just photograph). This makes the situation a bit more complicated. Bust, most of these laws are dealing with protection of privacy and “bugging” of conversations and in most of the cases audio recordings of the police is legal.
No court in the US has ruled that the police have a reasonable expectation of privacy, thus so long as they are in the public fulfilling their duty you have the right to record video.
Except: At the time of writing Illinois makes recording of police illegal regardless of expectation of privacy, but ACLU is currently challenging this based on a violation of the First Ammendment.