St. Jude Thaddeus* (usually known as just St. Jude) is the Patron Saint of difficult cases and lost causes. His feast day is October 28.
St. Jude is best known as one of the twelve Apostles of Christ and for The Epistle of Jude, the second to last book in the New Testament (See Jude). He was, in fact, a cousin of Jesus Christ, through the line of David (as I understand it, Jude and Christ were first cousins through their fathers and second cousins through their mothers). St. Jude should not be confused with Judas Iscariot.
St. Jude also spent a lot of time travelling and preaching the Christian Gospel to the non-believers in Judea, Samaria, Idumaea, Syria, Mesopotamia, and Lybia. We don't know for certain where or how he was martyred, but legend has it that he was clubbed to death in Armenia (then part of Persia) along with St. Simon. Hence, St. Jude is often pictured holding a club.
St. Jude is also often pictured holding image of Jesus in his hand. This is based on a story (or legend -- it doesn't appear in the Bible) telling of how Jesus entrusted St. Jude with taking a cloth imprinted with his image to the court of King Abagaro of Edessa, who was sick with leprosy. The cloth cured the king, and the king and his subjects converted to Christianity.
St. Jude's image also will usually include a tongue of flame over his head, to symbolize that he is one of the apostles who received the gift of the Holy Spirit on Pentecost.
His body is currently in crypt in St. Peter's Basilica, in Rome.
Prayer To St. Jude
To be said when problems arise or when one seems to be deprived of all visible help.
O, most holy apostle, St. Jude, faithful servant and friend of Jesus, the Church honours and invokes you universally, as the patron of hopeless cases, of things almost despaired of. Pray for me, I am so helpless and alone.
Make use I implore you, of that particular privilege given to you, to bring visible and speedy help where help is almost despaired of. Come to my assistance in this great need that I may receive the consolation and help of heaven in all my necessities, tribulations, and sufferings, particularly ( state request) and that I may praise God with you and all the elect forever.
I promise, O blessed St. Jude, to be ever mindful of this great favor, to always honour you as my special and powerful patron, and to gratefully encourage devotion to you.
* St. Luke (6:16) and St. John (14:22) refer to 'Jude'; St. Matthew (10:3) and St. Mark (3:18) refer to 'Thaddeus
'. It is generally held that they are referring to the same person, St. Jude Thaddeus.