How : Player move forward automatically (global Z axis) & 'not' the direction it's facing

     void FixedUpdate() {
             transform.position += transform.forward * Time.deltaTime;
             Turning    ();
     }
 
 
     void Update () {
 
                 float horizontalAxis = Input.GetAxis ("Horizontal");
                 float verticalAxis = Input.GetAxis ("Vertical");
 
 
                 if (controller.isGrounded) {
                     // We are grounded, so recalculate
                     // move direction directly from axes        
                     moveDirection = new Vector3 (0, 0, verticalAxis);
 
                     anim.SetBool ("run", true);
 
                     if (Input.GetKeyDown (KeyCode.UpArrow)) {
                         anim.SetTrigger ("jump");
                         moveDirection.y = jumpSpeed;
                     }
 
                 }
 
                 // Apply gravity
                 moveDirection.y -= gravity * Time.deltaTime;
 
                 // Move the controller
                 controller.Move (moveDirection * Time.deltaTime);
 

If you want to make it so that turning around doesn't change the way you're moving, you have to use Rigid body. Then you can toggle the "freeze position" option for x, y, & z (But be sure to only toggle the two you want) and remember to tune the "drag" parameter to suit your needs.

     float x;
     float y;
     private Rigidbody r;
 
     void Start()
     {
         r = transform.GetComponent<Rigidbody>();
         x = transform.eulerAngles.y;
     }
 
     void Update()
     {
 
         x += Input.GetAxis("Horizontal"); 
         y = Input.GetAxis("Vertical");
 
         //turn around without changing which direction to move
         Quaternion rotation = Quaternion.Euler(0, x, 0);
         transform.rotation = rotation;
 
         //move forward when you press "w" or "up"
         Vector3 forward = new Vector3(0.0f, 0.0f, y);
         r.AddForce(forward * 100);
         
     }

Instead of using Transform.forward use the Vector3 library:

 // Keep running forward no matter rotation
 transform.Translate ( Vector3.forward);
 

You Can use Vector3. Forward, Up and Right. If you want it Back, Down and Left just Multiply by -1:

 // Keep running backward no matter rotation
     transform.Translate ( Vector3.forward * -1);

Use this as your character controller:

 void Update () {
     // Will always keep running
    transform.Translate (Vector3.forward);
 }
 
 //Unity API Collision Function
 void OnCollisionEnter (collision other) {
    /* TODO: Write Code here to Do When Your Player Hits An Object */
 }