Old style city builders like Pharaoh, Caesar III, Zeus: Master of Olympus, Emperor: Rise of the Middle Kingdom, or Children of the Nile, but also the Stronghold and Tropico (as @Sargon mentioned 
) all incorporate judicial and police questions at some level. Mostly itâs just the building of courts and âpolice stationsâ, like in Pharaoh, but sometimes there is also a system of punishments and prevention, like in Stronghold, where the player builds structures to remind the citizens who is in charge, and that transgressions will be severely punished.
I know very little of concrete research in criminality in ancient or pre-ancient times, but I know that murder rates were much higher in pre-modern European societies. In societes where the state was weak, where getting caught was unlikely, and starvation a very common phenomenon, using force to attain certain resources, or security, was everything but rare. We see the same today, in societies where there is a state, but itâs very weak, and corruption is rife, and poverty great: Central America.
Thus I agree completely with @Elfryc writes, about the death penalty being much less frowned upon than in earlier times. God knows that the death penalty wansnât really questioned systimatically till the Enlightment of the 18th century.
Exiling, banishing, or ostracising, was very prelevant among the Greeks. Slavery was, to my knowledge, quite common among most sedentary advanced states from the Atlantic to the Indus, if not further (though I donât recognise it in ChinaâŠ? Before Qin, anyoneâŠ?). Indeed it continued in the Middle-East till the 20th century. But POWs in the modern sense are just that, a modern creation, brought forth by the growing internationalisation and large-scale warfare of the 19th and 20th centuries. Fredrick the Great of Prussia didnât have to care much about prisoners one way or the other, while the same was not true for his descendant Wilhelm II of Germany. Before that⊠everything mentioned in this thread seems to have been more or less prevalant depending on region. As @louis.mervoyer points out, the giving of ransoms did occur, which explains why his country was somewhat impoverished, and the English enriched, by the latterâs victories at CrĂ©cy and Agincourt.
So far, it seems that when it comes to fighting abroad, or generally fighting foreign foes, other tribes and alike, as discussed in World Map thread (World Map), the player should have the choice between:
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Executing all the prisoners (or the people inhabiting the city, village, or the tribe)
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Banishing, exiling, unsettling or deporting them, driving them away from what was formerly âtheirâ land, now âoursâ.
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Enslaving them, and either selling them outright on the spot, or taking them all back to the playerâs city, to work for us (or send them to our colony, a mine, to toil?)
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Assimilating them, by for example marrying each woman to our warriors, or killing off only the men of the right age, or something.
When it comes to criminality, meaning breaking the law here, at home, in the city, I guess what @Sargon points at in âhis ownâ empire is probably the norm: harsh justice. As the city grows and becomes quite advanced (which of coure is far in the future), I guess there would be system of courts, some form militia or military unit to keep the peace, and of course laws, which I hope the player would be able to change between different pre-defined position, for example:
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âWomensâ inheritance: none / meagre / substantial / equalâ
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âPrivate property: only the king / only nobles and priests / all citizensâ
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âSlavery: legal for criminals, debts and enemies / legal only for enemies / illegalâ
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âSlave status: inherited / not inheritedâ
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âCitizenship: only children of a citizen / only children of a citizen and persons of a certain wealth / any free personâ
⊠and many others.
Of course, the player should have the possibility to be a more âmildâ ruler, or rather a more âdraconianâ one, like in Stronhold, or Tropico. At times, mass crucifixions or Mongol style genocides might serve a purpose, as the Pax Mongolica suggests. Or even the first ever unification of Mesopotamia, @Sargon (unless Enshakushanna counts, but I think he used the same tactic, to the same result). Certainly, any threat to our regime should be dealt with swiftly and harshly, Tropico style. But otherwise, a milder law and execution thereof might be appropriate. Or as Hammurabi would have said, around 1700 BC: âto bring about the rule of righteousness in the land, to destroy the wicked and the evil-doers; so that the strong should not harm the weakâ.