Well, separation is always required; it can be achieved by following instructions from an air traffic controller, in which case the flight is controlled. It may be achieved by the pilots, in which case the flight is uncontrolled. In various types of airspace, various separation services are offered/mandatory for different flights.
For practical purposes, I fly into both controlled (towered) airports and uncontrolled (AFIS) airports; with the former the responsibility for separation primarily lies with the controller (say class D airspace), while in the latter the responsibility rests with me (class G airspace), however, the AFIS service will give me information in a pertinent way.
And IIRC VFR is not permitted in class A airspace...