Does any Jew have the 'right' to kill anyone he wants because he thinks the other is a rodef? I really don't think so. According to my understanding of the related laws, according to the story of Pinchas, we are not permitted to kill anyone at any time.
I believe in order to kill another Jew it is necessary to have the Sanhedrin find the offended guilty and a death sentence passed. In the case of a Rodef, as in the case of Pinchas, Pinchas was completely justified according to the Halacha.
But Judaism also has a number of commandments concerning respecting the Jewish king, not speaking badly about the Jewish courts and judges, etc.
http://www.chabad.org/library/article_cdo/aid/1088917/jewish/Chapter-One.htmHalacha 7What is implied? If the rodef was warned and continues to pursue his intended victim, even though he did not acknowledge the warning, since he continues his pursuit he should be killed.
If it is possible to save the pursued by damaging one of the limbs of the rodef, one should. Thus, if one can strike him with an arrow, a stone or a sword, and cut off his hand, break his leg, blind him or in another way prevent him from achieving his objective, one should do so.
If there is no way to be precise in one's aim and save the person being pursued without killing the rodef, one should kill him, even though he has not yet killed his victim. This is implied by Deuteronomy 25:11-12, which states: "If a man is fighting with his brother, and the wife of one... grabs the attacker by his private parts, you must cut off her hand; you may not show pity."
Halacha 8
There is no difference whether she grabs "his private parts" or any other organ that imperils his life. Similarly, the rodef may be a man or a woman. The intent of the verse is that whenever a person intends to strike a colleague with a blow that could kill him, the pursued should be saved by "cutting off the hand" of the rodef. If this cannot be done, the victim should be saved by taking the rodef's life, as the verse continues: "you may not show pity."
Halacha 9
This, indeed, is one of the negative mitzvot - not to take pity on the life of a rodef.
On this basis, our Sages ruled that when complications arise and a pregnant woman cannot give birth, it is permitted to abort the fetus in her womb, whether with a knife or with drugs. For the fetus is considered a rodef of its mother.
If the head of the fetus emerges, it should not be touched, because one life should not be sacrificed for another. Although the mother may die, this is the nature of the world.
Halacha 10
The laws of a rodef apply whether a person is pursuing a colleague with the intent of killing him, or a maiden that had been consecrated with the intent of raping her, as reflected by Deuteronomy 22:26, which establishes an equation between murder and rape, stating: "Just as when a man arises against his colleague and kills him, so too, is this matter i.e., the rape of a consecrated maiden."
The same principle is reflected by another verse within the passage, which states (Ibid.:27): "The consecrated maiden cried out, but there was no one to save her." Implied is that if there is someone who can save her, he must do so, using all means including taking the life of the pursuer.
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Halacha 13
When a person could prevent a murder or a rape by maiming the rodef's limbs, but did not take the trouble and instead saved the victim by killing the rodef, he is regarded as one who shed blood and is liable for death. Nevertheless, he should not be executed by the court.
Halacha 14
Whenever a person can save another person's life, but he fails to do so, he transgresses a negative commandment, as Leviticus 19:16 states: "Do not stand idly by while your brother's blood is at stake."
Similarly, this commandment applies when a person sees a colleague drowning at sea or being attacked by robbers or a wild animal, and he can save him himself or can hire others to save him. Similarly, it applies when he hears gentiles or mosrim conspiring to harm a colleague or planning a snare for him, and he does not inform him and notify him of the danger.46
And it applies when a person knows of a gentile or a man of force who has a complaint against a colleague, and he can appease the aggressor on behalf of his colleague, but he fails to do so. And similarly, in all analogous instances, a person who fails to act transgresses the commandment: "Do not stand idly by while your brother's blood is at stake."
http://www.chabad.org/library/article_cdo/aid/1088917/jewish/Chapter-One.htm