lexi and pyko share the games they love most, and why.
Portal. I know this is probably the first thing any puzzle-loving gamer would say, but it's true and I've yet to find a game that uses such a simple mechanic to such great effect. I mean, in the original game all you really have is two portals. What goes in one comes out the other. All you have to do is work out what that means in terms of physics. Like, "speedy thing goes in, speedy thing comes out". Now how do you use that to get to the exit? The (original) game doesn't overcomplicate things by throwing in more and more mechanics--it simply gets you to use the same portal mechanic in new and unexpected ways.
I could put a ton more games on this list, but I'll add Dishonored for its worldbuilding, and how much you can discover about the world and its history just by looking around and reading bits and pieces. I'll also say Journey, for the incredible atmosphere and the FEELS it evoked, The Swapper for another brilliant puzzle mechanic and stunning art, and Monkey Island 3 simply because it was one of the first point-and-click adventure games I played and it made me fall in love with the genre. There are so many others I want to name, but I won't in the interests of keeping things short(er)!
My favourite games share a common element: simple rules but complex strategy. They have basic concepts and rules that can lead to advanced/complex strategy and game play. Like lexi, Portal and Portal 2 are on my list, though Portal 2 is more for the co-op sections. It's amazing what you can do with double the portals!
The other one I love is Continuity. It's not well known, but it too has simple rules that end up creating a game which leaves you scratching your head. The core concept is simple: You're a stick figure on a frame which has a platform, there are other frames too (each with platforms). You slide the frames around so the platforms align so your character can move to the frame with the door. That's it. There's no fancy graphics required, or a long tutorial at the start—it simply introduces you to the core concepts and off you go. It really shows off how much you can do with so little.