What are the names of famous Christian martyrs?

Acts of the Apostles reports that Stephen was the first Christian martyr. However, Raymond E. Brown (An Introduction to the New Testament) says that the scene involving Stephen's trial and death is significant because it so closely resembles the story of the trial and death of Jesus in Luke. He says that we can never actually verify the existence and martyrdom of Stephen.

The martyrdom of James, brother of Jesus is well attested.

Christian tradition holds that all the disciples except John were martyred, usually in quite vivid and gruesome ways. However, scholars and even many modern theologians agree that there is no evidence for these traditions. The most famous of the traditions about the martyrdom of the disciples is the death in Rome, by crucifixion upside down, of Peter. However Clement of Rome, writing around 95 CE (1 Clement), spoke in general terms about the life and death of Peter but appears to have been unaware that he had even visited Rome or that he had been executed just a few years earlier. It seems that the tradition of Peter becoming the bishop of Rome, and of him being executed there, began with Pope Anicetus (156-166), who claimed that Peter had travelled to Rome to lead the Christians there and had been beheaded in Rome, meaning that he (Anicetus) spoke with the authority of the apostle Peter. Perhaps the beheading of Peter was not vivid enough, because Origen later reported that Peter had been sentenced to be crucified, but that not wishing to be killed in the manner of Jesus, asked to be crucified upside down.

The apostle Paul is also said to have been executed in Rome, at the same time as was Peter, but once again there seems to be no evidence for this. Clement of Rome seems to think that Paul actually travelled to Spain and spent his remaining years there.

The Apostolic Father, Polycarp was a famous martyr of the second century.