How do I get character to always face mouse?

My character is on the XZ plane, this is a topdown 2D game.
All that I want is that the character always faces the mouse, this shouldn’t be that hard.
Maybe I need to retake geometry, but this is actually REALLY confusing, can somebody help me out here?
It shouldn’t be that hard to make the character rotate to face the mouse (on the Y axis, I believe)…

like this:

I assume you have a plane representing the ground, with a collider… then just attach the following to your character (untested)

    function Update () {
            var hit : RaycastHit;
	        var ray : Ray = camera.main.ScreenPointToRay (Input.mousePosition);

            if (Physics.Raycast (ray, hit) {

RaycastHit hit;
Ray ray = Camera.main.ScreenPointToRay(Input.mousePosition);
if (Physics.Raycast(ray, out hit))
Debug.Log ("hit point " + hit.point);