It's a huge relief when the prosecution announces a decision not to file charges. But that doesn't mean the arrestee should do nothing further. In many instances, there are steps people can take to lessen, if not virtually eradicate, their criminal-law footprint. It's usually worth the effort, as a record of dealings with law enforcement can have painful effects, including when it comes to employment.
In California, for example, when someone has been arrested but not charged, the arrest is to be deemed a "detention" for all purposes; law enforcement is supposed to alter its records accordingly and the detainee is entitled to a certificate describing the arrest as a detention. But it may take action by the detainee—for example, affirmatively requesting a certificate—to get the full relief that is due.
In many states, whether or not the prosecution ever filed charges, some defendants are entitled to record-sealing pursuant to a finding of factual innocence. This procedure may involve filing a petition with the court, and even a hearing.
For more information on post-arrest relief, see Expungement or Sealing of Adult Criminal Records. (Many public defender websites also have helpful post-arrest information—for example, the Los Angeles County Public Defender.)
Most importantly, consult an experienced criminal defense attorney, as the procedure available to you depends on the facts and varies from state to state. Only a knowledgeable lawyer can advise you of all options, including your best course of action.