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);
	}
}

@Romaleks360 Loads of people around the web recommend caching strings in Unity optimization efforts. Check around.
Might be something more specific to the Unity Engine rather than C#.

Thank you so much I was making a flying camera for my game, and I had a problem where the z orientation kept changing. THIS FIXED IT! Again, thank you.

It pains me to say me too, not sure why the Quaternion.Euler() behaves that way.

Karl can you explain why perhaps the Quaternion.Euler() rotation creates off-axis rolls?

Thank you so much. Ive been struggling on this

Helped so much thank you! How would I hide my cursor?

here {

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(){
            **//Cursor.visible = false;**
	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);
}

}