Can I land a helicopter anywhere? If I own a helicopter and am appropriately rated, can I land the helicopter anywhere that isn't private property, and is a safe place to land (clear of obstructions, appropriate surface, etc.)?

My question is specifically about the regulatory requirements to land a helicopter off-airport in the United States.
Per §91.119 of the FARs, yes. That said, you can't just find an open field-there may be local/state regulations regarding helicopter operations.

14 CFR 91.119:


  (1) A helicopter may be operated at less than the minimums
  prescribed in paragraph (b) or (c) of this section, provided each
  person operating the helicopter complies with any routes or altitudes
  specifically prescribed for helicopters by the FAA