In the Star Trek: The Next Generation episode Reunion (#81), Worf kills Duras in retribution for killing his mate. Far from a clandestine operation, his behavior is discussed with Picard who informs him that a formal reprimand will be placed on his record.
This punishment seems disproportionately low compared to the crime. Is there some logical explanation for how a Starfleet officer can murder someone from another race in the line of duty and not be guilty of murder?
In that episode, Picard clearly acknowledges that what Worf did was legal under Klingon law.
PICARD: Mister Worf, your service aboard the Enterprise has been exemplary. Until now.
WORF: Sir, I have acted within the boundaries of Klingon law and tradition.
PICARD: The High Council would seem to agree. They consider the matter closed. I don't. Mister Worf, the Enterprise crew currently includes representatives from thirteen planets. They each have their individual beliefs and values and I respect them all. But they have all chosen to serve Starfleet. If anyone cannot perform his or her duty because of the demands of their society, they should resign. Do you wish to resign?
WORF: No, sir.
PICARD: I had hoped you would not throw away a promising career. I understand your loss, We all admired K'Ehleyr. A reprimand will appear on your record. Dismissed....
from Episode 81 ("Reunion") transcript at chakoteya.net.
It's explicitly not murder as Klingon law provides provisions for when revenge killing is lawful. As @Valorum states, there is probably some level of mutual respect on the part of the Federation toward Klingon culture that tempers the reaction significantly. In this case, Worf is not a fleeing international criminal or a fugitive from Klingon justice, just someone with a little need for further cultural assimilation.
In RL, there is the concept of double criminality which applies to extradition law and (I believe) immigration law as well. In a nutshell, it means that one country will consider someone from another country to be a criminal only if what that person did in the other country was illegal under the laws of both countries. So if a cocaine dealer from the UK goes to the USA, he is a criminal from the perspective of the USA.
In response to @BenOsborne 's question and @KyleStrand 's comment about why Picard did anything at all, there is a military law concept of "Conduct Unbecoming an Officer and a Gentleman" that is often an offense that is punishable but that is less serious than murder. In today's US military, "Conduct Unbecoming" may consist of (among other things)
...action or behavior in an unofficial or private capacity which, in dishonoring or disgracing the officer personally, seriously compromises the person’s standing as an officer; an officer’s conduct need not violate other provisions of the UCMJ or even be otherwise criminal to violate Article 133, UCMJ; the gravamen of the offense is that the officer’s conduct disgraces him personally or brings dishonor to the military profession such as to affect his fitness to command the obedience of his subordinates so as to successfully complete the military mission.
Source: Digest of the United States Court of Appeals for the Armed Forces (emphasis mine)
A revenge killing, even if legal in the jurisdiction in which it was done, could be seen as "dishonorable" to Worf in terms of his Starfleet career, and Picard even says so. The behavior impacts his career and how others perceive him in Starfleet. Here's the conflict of cultures inherent in Worf's position as a Klingon and a Starfleet officer - behavior that is allowed in one context is condemned in the other. Picard detects this and asks Worf how he proposes to handle it.
To piggyback on Robert Columbia's excellent answer, it's important to note that the crime occurred on the Klingon ship, and therefore likely under Klingon jurisdiction:
RIKER: Riker to Lieutenant Worf. Computer, locate Lieutenant Worf.
COMPUTER: Lieutenant Worf is not aboard the Enterprise.
PICARD: Where is he?
COMPUTER: Lieutenant Worf transported to the Klingon ship Vorn at seventeen thirty hours.
So regardless of whether Starfleet was inclined to accept Klingon cultural practices as lawful or not, it's not entirely clear that could have charged Worf if they wanted to, just as the German government can't punish me for murders in Baghdad.
I appreciate Robert Columbia's and tenthjustice's answer, but I read the dialogue between Picard and Worf somewhat differently.
To repeat the quotes from the other answers, just for completeness, we have first:
RIKER: Riker to Lieutenant Worf. Computer, locate Lieutenant Worf.
COMPUTER: Lieutenant Worf is not aboard the Enterprise.
PICARD: Where is he?
COMPUTER: Lieutenant Worf transported to the Klingon ship Vorn at seventeen thirty hours.
and later
PICARD: Mister Worf, your service aboard the Enterprise has been exemplary. Until now.
WORF: Sir, I have acted within the boundaries of Klingon law and tradition.
PICARD: The High Council would seem to agree. They consider the matter closed. I don't. Mister Worf, the Enterprise crew currently includes representatives from thirteen planets. They each have their individual beliefs and values and I respect them all. But they have all chosen to serve Starfleet. If anyone cannot perform his or her duty because of the demands of their society, they should resign. Do you wish to resign?
WORF: No, sir.
PICARD: I had hoped you would not throw away a promising career. I understand your loss, We all admired K'Ehleyr. A reprimand will appear on your record. Dismissed...
Worf left the Enterprise without requesting permission, or notifying his chain-of-command. The reason he did so is irrelevant. So Picard notes that whatever Worf did on the Klingon ship is not an issue for the Klingons, explains the proper procedure for dealing with a conflict between Klingon and Starfleet norms (resignation), asks if Worf wants to resign now (in effect asking Worf if he understands that he ought resign in the case of a future conflict), expresses sympathy for Worf's loss, and notes that a reprimand will be in Worf's record - and I interpret this as a reprimand for the minor transgression of leaving the ship without permission or notification. Note that 20 episodes later in Redemption, when there is another conflict between Starfleet norms (leave other societies to settle their own internal differences) and Klingon norms (I shall fight to make sure Gowron rules the Empire), Worf does resign (he's learned his lesson).
Aside from the cultural/legal considerations, there is another point- Duras is one of two Klingons suspected of slowly poisoning the previous chancellor K'Mpec, who warned his arbiter of succession- Picard, that a klingon underhanded enough to poison his way to the top could "be capable of anything- even war with the Federation".
Then there was an assassination attempt using a detonator known only to be used by the Romulans, whom Picard and the Enterprise officers know to have collaborated with the Duras family in the past (the bomb was revealed to have been implanted into one of Duras' men).
Put two and two together, and it is not hard to conclude Duras would be a threat to the Federation should he ascend to ruler of the Klingon Empire. Worf killing Duras, while not the ideal solution from a Federation perspective, did take care of the problem.
