I think there are 4 basic levels of intuitive: Intuitive, Counter-Intuitive, Obtuse and Unreasonable.
Dark Souls is (as far as I can remember) a mixture of intuitive and counter-intuitive, which is wonderful because everything can be figured out by doing the logical thing or its inverse.
Hotel Dusk was obtuse. For example there is a puzzle that requires you to dust a pen for fingerprints. To remove the excess dust you
. This was never mentioned previously, nor would anyone have a reason to believe it was even possible, but it could at least be attempted.
Braid is Unreasonable. The Secret Stars required for the best ending are so secret that they are never mentioned in the game whatsoever, and to get the complete set you need to wait for 2 hours in one level for a cloud to move into position. Even if you've somehow worked out that the Secret Stars exist, the cloud moves so slowly that it's practically immobile, and there is no way a player is going to hang out in one level for that long since most can be beaten in under 15 minutes.