For the uninitiated (although if you are reading this, chances are you're not) the prime directive states that "No starship may interfere with the normal development of any alien life or society." The most important law in Starfleet, it appears it is also the one most often violated.
Reading the directive the following is apparent:
1. It only applies to Starfleet personnel, not federation citizens
2. The nature of the interference is not qualified so any interference be it directly/indirectly would constitute a violation
3. It only relates to the normal development of alien life or society
Is it because of point 3 that Picard and Janeway conveniently overlooked the directive in cases where the society was enslaved or stagnated, thus not developing? Or is it just because the hereos can do no wrong? Just putting it out there. The only officer ever convicted of violating the prime directive appears to be Ronald Tracey (TOS- The Omega Glory).
An officer that violates the general order 1 may be court-martialed (see http://memory-alpha.org/en/wiki/Court_martial for more information on this process).
The prime directive does not apply where a civilization has already been exposed to alien species and information. It may also be violated where an extreme threat to the Federation exists.
Which brings me to TOS - A Taste of Armageddon. In this episode the USS Enterprise encounters two groups, the Eminiar and the Vendikar, who have been waging a war for many years using computer simulation. Victims in the simulation become real victims as those "hit" in the war have to report to disintegration stations within 24 hours to be executed. After ignoring a message from the planet to stay away the Enterprise enters the orbit and is "hit". As such, the crew has to report to the disintegration station.
Long story short: Kirk destroys several disintegration stations and has the war computers destroyed and so manipulates the Eminiar into breaking the treaty that governs the computer war. The Eminiar now have to either go into real war with the Vendikar or make peace.
A violation of the prime directive - definitely. Justified because of an extreme threat to the Federation? I submit not. They were told to stay away, and they went anyway. And the death of one ship's crew hardly constitutes an extreme threat. Surely an extreme threat would be the destruction of earth? Kirk's actions were totally motivated by self-preservation (you can read it on his face all through the episode) and a little by lust (Token blonde woman character was also "hit") and his violation of the prime directive was not justified. He should rather have left the planet and have gotten his crew out of harm's way. But then, that doesn't make for good tv.
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I find the permissable exceptions to the Prime Directive interesting. How does one determine that a culture has stagnated? If social development follows a similar model to biological evolution (which is a popular hypothesis), it's reasonable to expect long periods of 'statis' punctuated by brief periods of rapid change.
As a Starship captain, coming upon a culture that appears to have stagnated for some time (say, for several centuries) who am I to say that it would continue to remain static indefinitely? Odds are something would happen to disrupt the balance and necessitate change... no culture exists in a vacuum.
Of course one could argue that in the case of the Eminiar/Vendikar war, Kirk's actions were that something. But since Kirk deliberately took action, knowing full well what the consequences could be, he hardly qualifies as a statistical anomaly... I think he can more accurately be compared to an artificial selection pressure - that makes him something of a social engineer.
And, as I undertand it, social engineering is exactly what the Prime Directive is designed to prevent.
Succinctly put, Captain :)