The easiest way to move an object (G key) moves it parallel to the viewport.
BUT, is there any way to move it PERPENDICULAR to the viewport? That is, in depth but not just constrained to the XYZ axis/planes?
If you set the Transform Orientation to View, then GX, GY, GZ will translate in Screen space.. (Z being in and out of the screen).
Double-tapping the dimension (GXX, GYY, GZZ) will revert the translation to Global space, whichever orientation you have selected.