Is there any extra-biblical evidence that shows the apostles were martyred?

Question

Church tradition tells us that most of the 12 apostles were martyred, with the apostle John being the only one considered to die an old death.

Is there any extra-biblical evidence that shows the apostles were martyred?

Answer 1

If we count sources written multiple generations after the fact, there is mountains of evidence.

C. Bernard Ruffin has compiled a very thorough review of the traditions passed down by early Christian sources, acknowledging that not all of his sources are of equal weight, and some of the material written down many generations later is likely legendary in nature. His work on the subject can be found here: The Twelve: The Lives of the Apostles After Calvary.

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Solid, early sources

There are 4 men, named as apostles in the New Testament, for whom we have first century attestation of their death as martyrs:

• James the son of Zebedee (Acts 12:1-2)
• James the son of Joseph (Josephus, Antiquities 20.9.1)
• Peter (1 Clement 5)
• Paul (1 Clement 5)

3 of the 4 are attested by extra-Biblical sources.

Answer 2

Of the citations that Hold to the Rod mentions, only the one from Josephus is extra-biblical. {I misread "Rod's" post. Sorry... see his comment below) However, it is also the earliest IMO. This particular James was not strictly speaking an apostle, but he was clearly the leader of the Jerusalem church and called "brother of the Lord." Here's the passage:

...this younger Ananus, who, as we have told you already, took the high priesthood, was a bold man in his temper, and very insolent; he was also of the sect of the Sadducees, who are very rigid in judging offenders, above all the rest of the Jews, as we have already observed; when, therefore, Ananus was of this disposition, he thought he had now a proper opportunity [to exercise his authority]. Festus was now dead, and Albinus was but upon the road; so he assembled the sanhedrim of judges, and brought before them the brother of Jesus, who was called Christ, whose name was James, and some others, [or, some of his companions]; and when he had formed an accusation against them as breakers of the law, he delivered them to be stoned. {J. AJ 20.197}

Josephus also mentions the martyrdom of John the Baptist, who is recognized as a saint but not an apostle.

The OP asks for extra-biblical evidence as distinct from church tradition. This raises the question of the various Acts of the Apostles the tell of their deaths. These are extra-biblical, but they also feed into church tradition. The article "How Did the Apostles Die? What We Actually Know" summarizes them.