Dreamfall Chapters, Pillars of the Earth, and Pentiment are the first ones that come to mind. I really enjoyed all three. The Life is Strange games and the Telltale games are also kinda sorta similar.
Machinarium is a point-and-click puzzle adventure. I don't remember disliking the game, but I can't say I ever played it more than once.
There are the various Monkey Island remakes, if you're looking for something on the silly side. I haven't played any of them, the humor doesn't really click with me.
I want to try Procession to Calvary, it looks to be a Monty Python-style absurd point-and-click puzzler game.
