Six degrees of freedom

The ultimate example is Descent series. Spaceflight games often come close but surprisingly many are limited in one way or another (often limited to something similar to what fixed-wing aircraft have).

Requires ability to move on the 3 prime axises: forward/backward, left/right (strafe/sidestep), and up/down. And the capacity for pitch, yaw and roll.

Most 3D games are limited to 4 with 5th usually being in very limited form. Spaceflight games often omit the up/down and occasionally lef/right movement as well.

Automatic return to the galactic plane view are less interesting though still applicable if the controls are there.