How to avoid camera going upwards when looking up

I have made a simple scene and added this simple script to camera (it's for looking around and walking forward for now, I don't like using pre-made code):

 #pragma strict
 
 
 var mouse_x : float;
 var mouse_y : float;
 
 var sensitivity_x : float = 1.5;
 var sensitivity_y : float = 1.5;
 function Start () {
 
 }
 
 function Update () {
 mouse_x = Input.GetAxis ("Mouse X");
 mouse_y = Input.GetAxis ("Mouse Y");
 
 transform.Rotate(Vector3.up * mouse_x * sensitivity_x, Space.World);
 transform.Rotate(Vector3.left * mouse_y * sensitivity_y, Space.World);
 transform.eulerAngles.z=0;
 
 if (Input.GetKey (KeyCode.W))
 {
     transform.Translate(Vector3.forward * Time.deltaTime, Space.Self);
 }
 }

The problem is, when I look in the sky and press "W" (walk forward), the camera also moves in the sky. How do I avoid it and keep camera at the same level? I could probably set Z coordinate to some constant value, but then how would I move around a terrain?