The Christian Apostles were men who were (as indicated by the greek word apostolos) "sent forth", by Jesus after his resurrection, to preach the gospel to Jerusalem, Judaea and to the uttermost parts of the world (according to Acts chapter 1). The original twelve included Simon Peter, Andrew, James and John, the sons of Zebedee, Philip, Bartholemew, Matthew (a.k.a. Levi), Thomas (a.k.a. Didymus or "the twin"), James son of Alphaeus, Jude (a.k.a. Thaddaeus), Simon the Canaanite, and Matthias.
The attitude of the apostles, in the New Testament, towards Jewish people can be found here.
Judas Iscariot was one of the twelve disciples, but was never an apostle, since he killed himself before Christ's resurrection. Matthias was chosen by lot to replace Judas Iscariot. In his writings, Paul also claimed to be an apostle chosen by God; this claim has been generally recognized by the Church.
Some saints are given the title "equal-to-the-apostles." The myrrh-bearing women, who went to anoing 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.
The LDS Apostles are a council of men ordained by the LDS President to the highest order of authority except for the First Presidency.