During the 1st century Judah was a common name among Jews, and when Jesus called 12 men to become his apostles, he chose two with the name Judah. Based on the original Greek text this was rendered in Latin as Judas and for many centuries there wasn't a linguistic separator between Judas Iscariot and Judas Thaddeus.
As a result, early medieval Christians normally did not pray to the apostle Judas Thaddeus, because they were afraid of praying to Judas Iscariot, the traitor! Their fear was so great that Judas Thaddeus became one of the least known apostles.
Eventually the English language made a slight distinction between the two apostles and gave Judas Thaddeus the name Jude. Additionally, prior to this linguistic distinction St. Jude's intercessory power was revealed to various saints.
For example, according to writer Donald Thorman in his book St. Jude: Saint of the Impossible, "In one vision, Our Lord told St. Bridget to turn to St. Jude with a great deal of confidence, for, said the Lord, 'In accordance with his surname, "Thaddeus," the amiable, loving, he will show himself most willing to give help.' In another vision, Christ commanded the Swedish holy woman to dedicate an altar to St. Jude in her church. 'The fifth altar,' He said, 'must be for Thaddeus who with the purity of his heart will undoubtedly conquer the devil.'"
It's uncertain when St. Jude became associated with hopeless and impossible cases, but what is true is that countless miracles have been attributed to his intercession. His reputation for the impossible is so great, that he is known among a wide variety of Christians for his miraculous intercessory power.
Here is a common prayer to St. Jude that can be prayed for whatever impossible case you find yourself in.
Most holy Apostle, St. Jude, faithful servant and friend of Jesus, the Church honors and invokes you universally, as the patron of difficult cases, of things almost despaired of, Pray for me, I am so helpless and alone. Intercede with God for me that He 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 [make your request here] and that I may praise God with you and all the saints forever. I promise, O Blessed St. Jude, to be ever mindful of this great favor granted me by God and to always honor you as my special and powerful patron, and to gratefully encourage devotion to you. Amen.
