One particular Ancient Greek case is now a genuine icon of Western pop culture. The scene from 300 is based on a real event, described by our main source for the period:

To Athens and Sparta Xerxes sent no heralds to demand earth, and this he did for the following reason. When Darius had previously sent men with this same purpose, those who made the request were cast at the one city into the Pit and at the other into a well, and told to obtain their earth and water for the king from there.

-- Herodotos 7.133.1

But the movie tells this story in a very strange way. It presents the murder of the Persian messengers as Leonidas bravely taking a stand. His rejection of their proposal is so fateful and definitive that the death of the envoys says exactly the same as the message they would have carried to Xerxes. This is very far removed from the way Herodotos describes it: as one of the most terrible crimes ever committed by Sparta, which they begged Xerxes desperately to forgive them.

By Greek custom, all heralds and ambassadors were sacrosanct. They were the professionals who made peaceful interaction between states and peoples possible, and as such they were considered to be under the direct protection of Zeus, Hermes and the other gods. Any act of violence against a herald was an act of violence against the gods themselves. Those who killed messengers were thought to bring down a most severe, inescapable curse on themselves, their community and their state. And there was little that could terrify Greeks as much as the thought of going through life at the lasting displeasure of the gods.

The travel writer Pausanias gives a good idea of what the Greeks believed to be the consequences of killing a herald:

As you go to Eleusis from Athens along what the Athenians call the Sacred Way, you see the tomb of Anthemokritos. The Megarians committed against him a most evil deed, for when he had come as a herald to forbid them to encroach upon [the sacred land at Eleusis] in future, they put him to death. For this act the wrath of the Two Goddesses [Demeter and Persephone] lies upon them even to this day, for they are the only Greeks that not even the emperor Hadrian could make more prosperous.

-- Pausanias 1.36.3

The "even to this day" is the most telling part. The episode with Anthemokritos seems to have taken place in the second half of the 5th century BC. Pausanias is writing in the time of Emperor Hadrian - the 2nd century AD. The divine wrath, then, that the Megarians invoked by killing a single messenger, is supposed to have haunted them for more than five hundred years.

In other words, what the Athenians and Spartans did to the messengers of Darius was blasphemy; it was madness. The murder was an unforgivable sacrilege, and it was taken for granted that they would suffer a horrific punishment for their crime. Right after the lines cited above, Herodotos makes this clear in no uncertain terms:

What calamity befell the Athenians for dealing in this way with the heralds I cannot say, except that their land and their city were laid waste.

-- Hdt. 7.133.2

Even the fact that Athens was literally razed to the ground by the invading Persians was not enough for Herodotos to assume that the city had done its penance. That is how much of an interest he expected the gods to take in ruining Athenian lives.

So what about the Spartans? What price did they pay for their outrageous act? Herodotos says that they incurred the wrath of no other than Talthybios, the deified herald of Agamemnon from the story of the Trojan War - a bona fide god of messengers. For many years after they kicked the Persian envoys into the well, the Spartans could not get good omens from any of their sacrifices. Spartans were famously pious, and would not do anything if the omens were bad; a prolonged streak of this would have paralysed them as a state and as a community. At length, driven to despair and unable to figure out how else to appease the gods, they sent two volunteers to the Persian court to restore the balance. That is, they sent two men to Xerxes to beg for death. The pair travelled thousands of kilometers to plead with the Great King to execute them in turn, to atone for the sins of the Spartans. But Xerxes was better than his enemies:

Xerxes, with great magnanimity, replied that he would not imitate the Lakedaimonians. “You,” he said, “violate the laws of all humans by killing heralds, but I will not do that for which I censure you, nor by putting you to death in turn will I set the Lakedaimonians free from this guilt.”

-- Hdt. 7.136.2

Herodotos suggests that the willingness of the two Spartans to sacrifice themselves may have allayed Talthybios' anger for a while, but the curse was not truly lifted until a pair of Spartan messengers were caught and executed by the Athenians more than 50 years later, at the beginning of the Peloponnesian War.

This may be just a story in Herodotos, but we have no reason to believe that his notion of a common respect for messengers was not based in reality. There are no other examples from Greek history of messengers being murdered, even when the messengers are not Greek, or when they offer only tidings of misery and terror. Most scholars accept Xerxes' response as representative of actual Persian attitudes. It is difficult to imagine interstate relations of any kind, had their treatment of heralds been different. Heralds would not be harmed because, at the most practical level, their freedom to travel and speak could prevent wars and save lives; at a more religious level, those who harmed them would bring about the destruction of their own home and people.

I couldn't find an answer to this in the comments, so let me ask a dumb question.

If the Spartans knew it was so bad to kill the messengers, why did they... kill the messengers?

What a great question and top answer, fascinating!. Thank you to you both!