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In 2373 the USS Defiant was returning from a patrol mission in the Gamma Quadrant when it discovered a planet enclosed within some form of energy field. The ship passed through the field and discovered a colony of some 8,000 people on the surface. On beaming down, Captain Sisko was surprised to find that the colony was composed of the descendants of the Defiants crew! They told Sisko that when the ship took off in three days it would pass through an anomaly in the energy field which would throw it some 300 years into the past and disable the flight, causing it to crash. The survivors of the crash would found the colony.
Sisko was naturally reluctant to purposely crash his ship, but the colonists claimed to have a way to ensure that the energy field created a duplicate Defiant which would allow one version to crash and another to escape. However, it transpired that they were lying in order to ensure that the ship did in fact crash as it originally had. The crew initially wanted to leave the planet, but after spending some time with the locals they decided to go through with the crash in order to preserve the culture which had evolved there.
Unknownst to anybody in the colony or ship, Odo had decided to program the Defiants computer to avoid the anomaly. The Constable was in love with Kira Nerys, who had originally been killed after the crash. Odo was willing to sacrifice the 8,000 inhabitants in order to preserve her life. His plan worked, and the colony was erased from existence when the Defiant exited the energy field.
This event showed a large degree of poor thinking by the Defiants crew. Had the ship avoided the accident they would not be killing anybody as such; the colonists would never have existed in the first place. On the other hand, the very real friends and relatives of the Defiant crew would suffer from the loss of their comrades and loved ones. It was also suggested that account should be taken of those offspring who might be born to the crew if they continued with their normal lives, but this seemed to be a trivial concern next to those who were alive at that moment. Ultimately they decided that the loss of the Defiant was a price worth paying for preserving those lives.
Unfortunately, this fails to take into account the changes that had already been introduced. Given that the original crash was an accident, then the simple fact that the Defiant personnel were now aware of what was going to happen in the future would constitute more than enough change to create a timeline which would be significantly different. Once they had gained fore-knowledge of the accident, then the colony was essentially doomed no matter what happened and the best the Defiants crew could do would be to create a somewhat similar colony. However, in doing this they were essentially sacrificing real lives for hypothetical future lives - exactly the action that they had decided was not worthwhile earlier.
Temporal Investigations investigated this matter thoroughly and decided that no censure of the crew was needed, although Captain Sisko was required to take a refresher course in temporal logic. No further action has been taken and the case file has been closed.1