The Christian Apostles were Jewish men who were (as indicated by the Greek word apostolos) "sent forth", by Jesus to preach Christianity to both Jews and Gentiles, across the world.
The original 11 apostles
According to the New Testament, the eleven apostles chosen directly by Jesus Christ before his ascension were:
The 12th apostle
According to the New Testament, after the ascension of Christ, but before the day of Pentecost, these eleven apostles selected a twelfth apostle by casting lots. The lot fell upon Matthias, who then became the last of the "twelve apostles", taking the place of Judas Iscariot, who had betrayed Jesus. Judas Iscariot was one of the twelve disciples, but was never an apostle.
Additional apostles
In his writings, Paul also claimed to be an apostle chosen by God; this claim has been generally recognized by the Church. He is often known as the "Apostle to the Gentiles."
The writer of the Epistle to the Hebrews refers to Jesus as the first apostle of the Christian confession.
In the eighth century, the Anglo-Saxon St. Boniface was named the "Apostle to the Germans." In the ninth century, saints Cyril and Methodius earned the title "Apostles to the Slavs."
Some saints are given the title "equal-to-the-apostles." The myrrh-bearing women, who went to anoint Christ's body and first learned of his resurrection, are sometimes called the "apostles to the apostles" because they were sent by Jesus to tell the apostles of his resurrection.
Discussion of anti-Semitism
Most Jews and many liberal Christians believe that the statements of some of the apostles, as quoted in the New testament were anti-semitic. This controversial subject is dicussed in detail in its own entry, Christian_anti-Semitism.
LDS Theology
In the LDS Church Apostles are a council of fifteen ordained men who are called to hold the highest Priesthood authority in the LDS Church for life. Typically, the most senior member of the group is also ordained as the President and Prophet of the LDS Church. The President is supported by two Apostles who are his Counselors. The Prophet and his two Counselors compose the First Presidency. The remaining Apostles compose the Quorum of the Twelve Apostles, the most senior member of that quorum being the President of that quorum. As vacancies arise, all of the Apostles meet to pray and to come to a unanimous decision as to whom among the rank and file of the LDS Church will be called to fill the vacancy. The Apostles will then ordain the next man called to be an Apostle. The Quorum of the Twelve Apostles is equal in authority to The First Presidency. In LDS theology when Christ personally reigns on the earth, He will personally take the place of the office of the First Presidency.
See also apostolic succession -- New Testament