Those who live by the trope, and dice by the trope, well... get bored and look around for a new game to play.
I like to throw a puzzle in every now and then, but the problem is it can get hokey. (And a stripper with a medusa-head only works if your players are 13.)
Know what I mean?
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The great challenge of our modern education system is that it does not take the three C's into account in the education of children. Namely, Character development, Critical Thinking, and Conflict Resolution.
In a fantasy game (or sci-fi too, for that matter), a puzzle always challenges at least one or more of the above principles.
Themes for Puzzles:
Character Development: Self-sacrifice, Moral Decision Making, Visions of the Past or Threats of the Future, Painful Memories, Challenged Relationships. The Sacrifice of the One for the Many, Riddles With No Correct Answer
Critical Thinking: Basic Logic, Assumption, Awareness of Awareness, Social and Cultural Expectations vs Reality, Challenge Currently Held Perspectives, Conflicts of Religious Teachings, Riddles With More Than One Correct Answer
Conflict Resolution: An Item of Interest to Many, Two Paths (One Way), Alignment Debate, Truth or Lies (a classic, perhaps overused), Group Deception and/or Manipulation, Authority Deception and/or Manipulation, Divine Deception and/or Manipulation. Seemingly Impassible Block, Riddles With Only One Correct Answer.
Generally, you could take a few ideas for puzzles from those listed above, or combine more than one into a single puzzle.
The sphinx relates you a riddle, wizard what do you do?
4 for int; 2 for headband of intellect, 8 for knowledge: logic puzzles,
The answer is Man!
<Brain fart>
RPG Superstar Season 9 Top 16, RPG Superstar 2015 Top 32
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last Summer I ran a game for a group of High School students. In this game I presented them with a major non-combat situation and a combat situation every session. Each one was designed to challenge their problem solving and decision making abilities while having fun at the same time.
Some examples:
A river crossing at a very dangerous part of the river. This might not sound like a big challenge, but the acrobatics DC was high to leap across rocks, the Swim check was high enough that some of the characters would have trouble, and the there was a time limit. In the end, they worked out a plan that let them work together to create a bridge.
A dungeon built into a cave system with many, many false passages that led on for deceptive distances. In this dungeon there were several larger chamber, each one with a different challenge to overcome. One had a powerful undead that demanded answers to riddles. One was one large puzzle trap that tested the groups ability to work together while taking damage. Another had powerful guardian that challenged them to a game of wits. One room was sectioned off and had traps that would not only damage the target, but put them back to the beginning of the chamber. I did not allow anyone to use ability or knowledge checks to figure out the puzzles. The last challenge came when they reached the end of the dungeon and it started to flood. They then had to navigate all the way back to the beginning quickly, avoiding any false turns along the way. They almost didn't make it.
To simulate a character with an extremely high intelligence, I would sometimes present a puzzle to the whole group of players and let them work it out at a meta level. The answer that they would arrive at as a group would represent the in world resolution put forth by the character with the high intelligence stat. My group seemed to like that; they all got to participate but it made sense in the game too. It also helped if the player with the high INT character wasn't necessarily the brightest IRL.