A simple First Person Camera rotation script for Unity.

FirstPersonCameraRotation.cs

using UnityEngine;

/// <summary>
/// A simple FPP (First Person Perspective) camera rotation script.
/// Like those found in most FPS (First Person Shooter) games.
/// </summary>
public class FirstPersonCameraRotation : MonoBehaviour {

	public float Sensitivity {
		get { return sensitivity; }
		set { sensitivity = value; }
	}
	[Range(0.1f, 9f)][SerializeField] float sensitivity = 2f;
	[Tooltip("Limits vertical camera rotation. Prevents the flipping that happens when rotation goes above 90.")]
	[Range(0f, 90f)][SerializeField] float yRotationLimit = 88f;

	Vector2 rotation = Vector2.zero;
	const string xAxis = "Mouse X"; //Strings in direct code generate garbage, storing and re-using them creates no garbage
	const string yAxis = "Mouse Y";

	void Update(){
		rotation.x += Input.GetAxis(xAxis) * sensitivity;
		rotation.y += Input.GetAxis(yAxis) * sensitivity;
		rotation.y = Mathf.Clamp(rotation.y, -yRotationLimit, yRotationLimit);
		var xQuat = Quaternion.AngleAxis(rotation.x, Vector3.up);
		var yQuat = Quaternion.AngleAxis(rotation.y, Vector3.left);

		transform.localRotation = xQuat * yQuat; //Quaternions seem to rotate more consistently than EulerAngles. Sensitivity seemed to change slightly at certain degrees using Euler. transform.localEulerAngles = new Vector3(-rotation.y, rotation.x, 0);
	}
}