I tend to run puzzling plot elements on the background, but which are not necessarily needed for the game proceed. However, so far I've used two actual "dungeon puzzles" worth mentioning in my campaign.
1) In Pteion, there was a chamber with four doorways, one of which the player group entered from. As they were inside, the doorways were blocked with heavy stone slabs. On them was writing about history of the world and Stygia in particular. There was a moving part in the stone slabs that had to be pushed in a chronological order. Doing so in wrong order was punished by poison gas being blown in the chamber. Things mentioned in the texts were stuff a blind storyteller had told the characters about several sessions earlier, so the players had to rake their memories for clues.
2) While robbing an ancient Acheronian tomb in Tartarus, underneath Messantia, the characters came in to a hallway that contained entrances to six tombs, with six statues near the doors. In the middle of the hallway was an ancient well. Once they had spent some time in the room, the entrances were sealed with heavy stones and water started pouring forth from the well. The characters (and again, players) had to deduct what the statues symbolize and pull their arms in right order while the torrent of water was getting even heavier. They had a quite tight time limit in this one, with serious prospects of drowning.
