MouseLookScript.cs

using UnityEngine;
using System.Collections;

public class MouseLookScript : MonoBehaviour {

	[HideInInspector]
	public float xRotation;
	[HideInInspector]
	public float yRotation;
	public float lookSensitivity = 5;
	[HideInInspector]
	public float currXRotation;
	[HideInInspector]
	public float currYRotation;
	[HideInInspector]
	public float xRotationVelocity;
	[HideInInspector]
	public float yRotationVelocity;
	public float smoothDampTime = 0.1f;

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

		xRotation -= Input.GetAxis ("Mouse Y") * lookSensitivity;
		yRotation += Input.GetAxis ("Mouse X") * lookSensitivity;

		xRotation = Mathf.Clamp(xRotation, -90, 90);

		currXRotation = Mathf.SmoothDamp(currXRotation, xRotation, ref xRotationVelocity, smoothDampTime);
		currYRotation = Mathf.SmoothDamp(currYRotation, yRotation, ref yRotationVelocity, smoothDampTime);

		transform.rotation = Quaternion.Euler(currXRotation, currYRotation, 0);
	}
}