Charactercontroller.move affecting rotation

SimpleMove and Move both expect a global direction, not local. The difference between them is that SimpleMove expects the velocity vector, while Move wants the displacement. I suspect that you're using the example scripts - they are different: the SimpleMove example rotates with the horizontal arrows, while the Move example rotates with the mouse and moves laterally with left/right keys. If this is the case, you must create a "Frankenstein" script with parts of both - like this:

 var speed : float = 6.0;
 var rotSpeed : float = 90.0; // rotate at 90 degrees/second
 var jumpSpeed : float = 8.0;
 var gravity : float = 20.0;
 private var moveDirection : Vector3 = Vector3.zero;

 function Update() {
     // rotate character with horizontal keys:
     transform.Rotate(0, Input.GetAxis("Horizontal") * rotSpeed * Time.deltaTime, 0);
     var controller : CharacterController = GetComponent(CharacterController);
     if (controller.isGrounded) {
         // We are grounded, so recalculate
         // move direction directly from axes
         moveDirection = Vector3.forward * Input.GetAxis("Vertical");
         // convert direction from local to global space:
         moveDirection = transform.TransformDirection(moveDirection);
         moveDirection *= speed;
         if (Input.GetButton ("Jump")) {
             moveDirection.y = jumpSpeed;
         }
     }
     // Apply gravity
     moveDirection.y -= gravity * Time.deltaTime;
     // convert velocity to displacement and move character:
     controller.Move(moveDirection * Time.deltaTime);
 }