FlyCam.cs

using UnityEngine;

public class FlyCam : MonoBehaviour
{

    public float speed = 1;
    public float mouseScrollAccel = 2;

    public bool localRotation;

    public float mouseSensitivity = 100.0f;
    public float clampAngle = 80.0f;

    private float rotY = 0.0f; // rotation around the up/y axis
    private float rotX = 0.0f; // rotation around the right/x axis

    float initSpeed;
    float speedScrollMult = 1;

    public bool inFixedUpdate;

    [Header("Control")]
    public bool useNumpadArrows = true;
    public string horizontalAxisName = "Horizontal";
    public string verticalAxisName = "Vertical";

    void Start()
    {
        Vector3 rot = transform.localRotation.eulerAngles;
        rotY = rot.y;
        rotX = rot.x;

        initSpeed = speed;
        speedScrollMult = Mathf.Sqrt(initSpeed);
    }

    void Update()
    {
        float scroll = Input.GetAxis("Mouse ScrollWheel");

        if (scroll != 0)
        {
            speedScrollMult += scroll * mouseScrollAccel;
            if (speedScrollMult < 0) speedScrollMult = 0;
            speed = speedScrollMult * speedScrollMult;
        }

        if (!inFixedUpdate)
            DoMouseLook();
    }

    void FixedUpdate()
    {
        if (inFixedUpdate)
            DoMouseLook();
    }

    void DoMouseLook()
    {
        float mouseX = Input.GetAxis("Mouse X");
        float mouseY = -Input.GetAxis("Mouse Y");

        rotY += mouseX * mouseSensitivity * Time.deltaTime;
        rotX += mouseY * mouseSensitivity * Time.deltaTime;

        rotX = Mathf.Clamp(rotX, -clampAngle, clampAngle);

        Quaternion rot = Quaternion.Euler(rotX, rotY, 0.0f);

        if (!localRotation)
            transform.rotation = rot;
        else
            transform.localRotation = rot;

        float z = 0;
        float x = 0;

        if (useNumpadArrows)
        {
            x = Input.GetKey(KeyCode.Keypad4) ? -1 : Input.GetKey(KeyCode.Keypad6) ? 1 : 0;
            z = Input.GetKey(KeyCode.Keypad2) ? -1 : Input.GetKey(KeyCode.Keypad8) ? 1 : 0;
        }
        else
        {
            z = Input.GetAxis("Vertical");
            x = Input.GetAxis("Horizontal");
        }

        transform.Translate(Vector3.forward * z * speed * Time.deltaTime, Space.Self);
        transform.Translate(Vector3.right * x * speed * Time.deltaTime, Space.Self);
    }
}