More complex than BasicFly.cs, cannot be placed directly on a camera, but instead requires a camera as a child. This script still moves using Transform.Translate (so will fly through colliders). Uses <space> and <shift> to rise or fall, and flies flat regardless of the vertical camera pitch. Designed to work similar to the Minecraft camera.

SimpleFly.cs

using System.Collections;
using System.Collections.Generic;
using UnityEngine;

public class SimpleFly : MonoBehaviour {
	public float rotationSpeed = 100.0f;
	public float moveSpeed = 100f;
	public float viewRange = 45f;

	private Transform cameraTransform;
	private float yaw = 0f;
	private float pitch = 0f;

	// Use this for initialization
	void Awake() 
	{
        #if UNITY_EDITOR
        	Cursor.lockState = CursorLockMode.None;
        	Cursor.visible = true;
        #endif
        
        #if UNITY_STANDALONE
        	Cursor.lockState = CursorLockMode.Locked;
        	Cursor.visible = false;
        #endif

		if(gameObject.GetComponent<Camera>() != null)
		{
			throw new UnityException("This script should not be placed on the camera.  Instead put this script on the parent of the camera.");
		}

		Camera camera = gameObject.GetComponentInChildren<Camera>();
		if(camera == null)
		{
			throw new UnityException("Must have a Camera as a child object");
		}

		cameraTransform = camera.transform;
	}

	// Update is called once per frame
	void Update () {

		yaw += Input.GetAxis("Mouse X") * rotationSpeed * Time.deltaTime;
		pitch -= Input.GetAxis("Mouse Y") * rotationSpeed * Time.deltaTime;
		pitch = Mathf.Clamp(pitch, -viewRange, viewRange); 

		transform.eulerAngles = new Vector3(0f, yaw, 0f);
		cameraTransform.eulerAngles = new Vector3(pitch, yaw, 0f);

		Vector3 moveDir = transform.forward * Input.GetAxis("Vertical") * moveSpeed * Time.deltaTime;
		moveDir += transform.up * Input.GetAxis("Jump") * moveSpeed * Time.deltaTime;	
		moveDir += transform.right * Input.GetAxis("Horizontal") * moveSpeed * Time.deltaTime;
		
		if(Input.GetKey(KeyCode.LeftShift))
		{
			moveDir -= transform.up * moveSpeed * Time.deltaTime;	
		}

		if(moveDir.magnitude > 0f)
		{
			transform.Translate(moveDir, Space.World);
		}
	}
}