Special considerations when videotaping:
With regards to videotaping, there is an important legal distinction between a visual photographic record (fully protected) and the audio portion of a videotape, which some states have tried to regulate under state wiretapping laws.
Such laws are generally intended to accomplish the important privacy-protecting goal of prohibiting audio "bugging" of private conversations. However, in nearly all cases audio recording the police is legal.
In states that allow recording with the consent of just one party to the conversation, you can tape your own interactions with officers without violating wiretap statutes (since you are one of the parties).
In situations where you are an observer but not a part of the conversation, or in states where all parties to a conversation must consent to taping, the legality of taping will depend on whether the state's prohibition on taping applies only when there is a reasonable expectation of privacy. But no state court has held that police officers performing their job in public have a reasonable expectation.
The ACLU believes that laws that ban the taping of public officials' public statements without their consent violate the First Amendment. A summary of state wiretapping laws can be found here.