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I feel that the games that take the most quick thinking are competitive online games that involve a lot of strategy. I will probably get laughed at for suggesting something like Starcraft 2 , but the thing is, the better the competition, the more challenging it gets.
Of course there are a lot of puzzle games as well, but imo there are more fun games you can play. For me personally, the most interesting and diverse way of being challenged is when playing against an actual person. Chess would be the most obvious example, and probably the first "competitive" game I ever played.
Even now, a game like DOTA2 even though the community is thought of as being full of idiots, is more interesting for me in terms of quick thinking and being challenging, than something like Myst of Age of Empires. Note that there are different brackets of competition, and people who stay in "normal bracket" probably have no valuable input as to whether the game requires you to think or not.
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