What kind of puzzles do you give your players?

[Korgoth]

I have also had my players request more puzzles. Unfortunately, as others have mentioned, puzzles are very hard to work in believably.

"Believably"? I know, I know... but forget elfs and wizards and fire-breathing flying dragons... dungeons themselves are unbelievable.

Anyway, I think the point of the dungeon is to challenge the players, not the characters. The characters can get challenged or not based upon a mathematical analysis and/or balancing act on the part of the DM. That's just math... nothing more, nothing less.

To me the real fun is to make the players have to exercise their minds. So I don't mind throwing in Fibonacci sequences and puzzles that rely on modern principles of chemistry, optics, etc.

Ultimately, it only comes down to this: is the situation set up so that only the lucky die-rollers win, or is it set up so that only the smarties win. I like to play games oriented toward the latter.

Though that is not to deny that there's always an element of risk management. But back to the point about realism and believability... risk management is metagaming as well. I've stopped seeing metagaming as a bad thing. In a lot of ways, it is the game.

 

[Almacov]

The closest things to puzzles that typically wind up in my games are more like mysteries or decisions that have to be made in exploration.

The first example I can (fuzzily) recall is from what was probably the earliest game I DMed. (As such, it's not a shining example. =P)

The party was infiltrating a goblin stronghold and came upon either a locked door, or an un-raised bridge. There was a room before this point that contained several goblins guarding a captive... mite, I think. In any case, the mite had seen the goblins open the door/raise the bridge, and thus knew how it was accomplished. If they kept him alive, they could gain this information.
The locking mechanism consisted of three holes- one about the height of a goblin head, two about goblin waist height.
Putting living matter in each of these activated it, and if one's head were placed in the top hole, a beam of light shot out of if and generally into the person's face. This did several points of wisdom damage, as well as allowing the threshold to be passed and relaying some information psionically to the blue that was running the place.

I ran this adventure twice, and each time the players did something different. One set forced the mite to activate the device, and I'm pretty sure another had a party member do it. There were a bunch of other juvenile and tricky bits in the complex, and while it was a bizarre and impractical design, it was always kindof neat to see how the players would work around each obstacle.

Nowadays my adventure design is in some ways less creative... I sortof miss being in elementary school.