The standard mouselook seems a bit inefficient to me, so I made one.
Setup is dead simple, just have a look at the .blend.
If you parent the camera to an object, it will stay relative to that object.
It can start at any orientation.
It has variable sensitivity and up/down view limiting.
And obviously, you can use it on any game object, not just a camera.
Enjoy, and happy blending! I’m open to suggestions and problem reports.
Edit: Drifting issue fixed thanks to Rhys of GB.org. Files updated.