The twelve apostles are Peter, Andrew, James (son of Zebedee), John, Philip, Bartholomew, Thomas, Matthew, James (son of Alphaeus), Thaddeus, Simon (the Zealot), and Judas.
As you indicate, Judas took his own life (Matt. 27:1-5), and St. John, the son of Zebedee, was assigned by Jesus to take of his mother Mary (John 19:25-27), and a strong tradition holds that he later died of natural causes at an old age in Ephesus.
Scripture conveys that James (the Greater), the son of Zebedee, was martyred by King Herod Agrippa I (Acts 12:1-3), although the king himself was struck dead by an angel not long afterward (Acts 12:19-23). There is abundant testimony in the early Church that St. Peter, who was imprisoned on the occasion of James’s execution (Acts 12:3), was martyred around twenty years later in Rome, along with St. Paul.
St. James (the Lesser), son of Alphaeus, is often identified with St. James, “the brother,” i.e., relative, of Jesus, the bishop of Jerusalem noted in Acts 15, was who martyred by stoning in Jerusalem in the A.D. 60s, as Eusebius testifies (Church II, 23), and also Josephus, the noted Jewish historian of antiquity. As Pope Emeritus Benedict XVI has stated, “Among experts, the question of the identity of these two figures with the same name, James son of Alphaeus and James ‘the brother of the Lord,’ is disputed.”
We also see that tradition holds that St. Thomas preached in India and suffered martyrdom there, as Pope St. John Paul II affirmed in his 1986 apostolic visit. In addition, tradition holds that St. Andrew was martyred via a form of crucifixion around A.D.60.
St. Bartholomew—also understood by many scholars as “Nathaniel”—is also believed to have been martyred, reportedly either by beheading or being flayed alive.
St. Philip may have been martyred in Hierapolis (located within modern-day Turkey), although that may be the tomb of St. Philip the deacon, noted in the Acts of the Apostles.
St. Matthew, The Roman Martyrology conveys, was martyred, although the manner of his death is disputed.
Finally, tradition also holds that St. Simon (the Zealot), the son of Clopas and who is also called Jude, was martyred, as was his apostolic companion, St. Jude (Thaddeus). They are both listed in the Roman Martyrology and the Roman canon (Eucharistic Prayer I).