Do you have any unusual ways to punish or execute criminals in your games? Please share...
I find the reality of ancient judicial punishments to be far more bizarre than anything I could actually imagine. Many of them I would not even want to portray in game. The mores on display are so far from modern notions that I feel pretty sure that if I even make note of them, someone would consider them either an endorsement of those beliefs or else a sort of psychopathic voyeurism.
I tend to deal with this problem by having the dominate religious system have a more modern notion of justice, while the more historically accurate notions of 'justice' are represented by older outlawed cults - bad guys in other words. But even then, there are plenty of areas you can be fairly gray on compared to modern ideas - torture, death by exposure, burning at the stake, and beheading are generally usual and accepted even in societies that are nominally 'good' leaning in the setting. I try to reference how harsh the world is without really trying to dwell on it in the imagination graphically. Nonetheless, the PC's have witnessed judicial torture twice in the current campaign, and seen persons convicted of looting in the aftermath of a natural disaster condemned to death by gibbetting - the idea being that this was a 'just' punishment because their greed might condemn the unfortunate to the very death that they now suffer. Likewise, though they didn't witness it, a man found guilty of multiple homocides was drawn and quartered - considered fitting because he'd dismembered the bodies of those he killed.
I know in other parts of the world, that criminals are often executed in trials by combat intended to be public spectacles. In the past, criminals were often executed by energy drain in certain cultures, with the energy collected in magical batteries used to power public works or defenses. However, unless the execution serves some other public purpose, I'm skeptical that expensive methods like this would be used. Weaponized magic is expensive, and unless it serves some other public good, expensive methods of execution would tend not to be used for simple economic reasons. Still, I can recall reading a fantasy story that featured an animated guillotine as the key instrument of execution, which seems rather reasonable and flavorful if you can manage it.
Certain sorts of execution methods that were historically used might not be in favor in a society with widespread magic. If something like 'death by falling' can be thwarted not just by divine intervention, but with a simple feather fall spell, they aren't likely to see much use. I think of the problems of trying to execute the five brothers in the fairy tale. Society is likely to default to forms of execution that are very hard to evade generally, and have safeguards against the use of magic to as great of extent possible. Accused individuals that are potential spellcasters are treated very harshly - eyes burned out with heated copper, fingers broken, tongues torn out, etc. - simply because people are terrified of them.
Even that sort of brutality depicted frankly at a gaming table for me runs right up against the line. I have a strong reason for it, and only depict that sort of thing with adults. And yet, as brutal as that sort of thing is, it doesn't even begin to touch the true perversity - or 'creativity' if you prefer a more neutral term - of ancient judicial punishments. I personally would feel a bit... unclean.. applying my creativity seriously to the problem of making weird forms of execution or punishment. It's bad enough that I know some of the things people have done to each other, and in some cases still do to each other.