An apparatus for drilling curved and straight sections of a wellbore is disclosed that in one non-limiting embodiment includes a drilling assembly configured to include a drill bit at an end thereof that can be rotated by a drive in the drilling assembly and by the rotation of the drilling assembly, and wherein the drilling assembly includes: a deflection device that (i) tilts a section of the drilling assembly within a selected plane when the drilling assembly is substantially rotationally stationary to allow drilling of a curved section of the wellbore by rotating the drill bit by the drive; and (ii) straightens the section of the drilling assembly when the drilling assembly is rotated to allow drilling of a straight section of the wellbore.