Socrates is considered to be the most famous example of Noble Death as well as the first martyr because instead of going into voluntary exile to escape the fate of execution, he chose to die by drinking hemlock. According to Epictetus Socrates redeems himself by dying and not by running away. Plato also mentioned that the philosopher should welcome death, since through it one attains the greatest blessing (Middleton, 8).
Socrates is an important example of resistance to a tyrannical authority (Moss, 24). The Death of Socrates in 399 bce, narrated originally by Plato, had been adapted and reinterpreted before its use by early Christians and because Socrates was held in a high regard by generations of Greeks and Romans, Christians viewed him in a similar positive light (Moss, 25). The legend of Socrates was formed by his succession of disciples as well as his various biographers and the end result was a figure shaped by hearsay, slander as well as adoration (Moss, 33). This is why it is difficult to separate the man from the myth.
According to Plato, Socrates was a noble man, unfairly charged with atheism, who refused to flee death in order to go into exile. He embraced death calmly, even insisting on silence and became in death, a model for other followers (Moss, 34). According to Socrates dying well is important to the philosopher and in fact "the true philosopher practices dying and death is less fearful to them than to any other man" (Phaed. 67 e). According to Moss, Socrates' passive countenance casts him as the classical embodiment of masculine self-control (34).
Zeno was considered a noble man in both philosophy and citizenship according to Van Henten and AveMarie. After he bit off his own tongue (as a gesture that he would never give up the names of his accomplices) and spot it out in the face of Nearchus, the citizens were so moved that they apparently stones the tyrant to death (Van Henten, 26).
Anaxarchus was arrested by Nicocrean in Cyprus and after he was ordered to be beaten and have his tongue cut out (most likely for what he said at dinner with Nicocrean), like Zeno he bit off his own tongue voluntarily and spit it out at Nicocrean (Van Henten, 27). Spitting at the tyrannical authority must be a bit of a theme in Greco-Roman literature/legend. I can see why it's so popular though, since it's very disrespectful and sends a strong message.
Apollonius of Tyana faced charges in Rome for conspiracy against the emperor Domition. In a conversation with Demetrius and Domius, they discuss whether or not Apollonius should go to Rome and face the charges or run away (I presume). Demetrius believes that a philosopher should die in an attempt to liberate his city, protect his parents, children, brothers and other kin as well as for his friends. However he believes that it is wrong to be put to death or die voluntarily for untrue reasons or "fancy" ones (Philostratus, 12). Domius believes that one should die for the cause of philosophy, meaning that they should die for their temples, walls, and sepulchers. He argues that there were many heroes that died in order to protect and save interests such as these (Philostratus, 13).
Apollonius then said "I would indeed have a wise man sacrifice his life for the objects you have mentioned, but any man without being wise should equally die for them; for it is an obligation of law that we should die in behalf of our freedom, and an injunction of nature that we should die in behalf of our kinsfolk or of our friends or darlings. …" (Philostratus, 14). Apollonius then goes on to mention that "...I run no risk of my life myself, nor shall I die at the hands of a despot, however much I might wish to do so; but I am aware that I am gambling with the lives of those whom I bear such relation; the tyrant chooses, whether he count me their leader or their supporter" (Philostratus, 14). He believes that if he were to hold back or refuse to face the accusation like a coward, he would be betraying his people and no longer thought of as a good man but rather a traitor.