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?
You have to set the transform orientations to "view", then press G Z, move the mouse and confirm with left click.
If your view is orthographic you will not see any apparent movement but you can read the distance you're moving in the top left corner of the 3D window.
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.