One of the famous stories of St. Martin is about his dealing with the Priscillianists. The Priscillianists were Gnostics and therefore heretics; they were sanctioned by the Emperor Maximus and the leader, Priscillian, but on trial. Martin went before the Emperor to persuade him that heresy should not be tried in secular courts, and to make Maximus promise not to allow the death sentence in the case. Priscillian was sentenced to death anyway. Martin returned to try to protect some of Priscillian's followers. (St. Martin wasn't the only Catholic to protest the treatment of the heretics; both Ambrose of Milan and Pope Damasus protested the action, and the bishop Ithacius, who had led the prosecution, found himself suddenly isolated, with the Gallicans breaking off communion with him and the Iberians eventually deposing him for stirring up the interference of the government in an ecclesiastical matter.)
The most famous legend about St. Martin, though, is the legend of the cloak. While a soldier at Amiens, about 20 years old or so, he met a poor beggar at the city gates; Martin had no money, but the man looked cold, so Martin cut off half of his cloak with his sword and gave it to the man. That night he had a dream of Jesus wearing the half-cloak and saying to the angels, "Here is the unbaptized Martin; he has clothed me." As Sulpicius Severus puts it:
The Lord, truly mindful of his own words (who had said when on earth -- "Inasmuch as ye have done these things to one of the least of these, ye have done them unto me"), declared that he himself had been clothed in that poor man; and to confirm the testimony he bore to so good a deed, he condescended to show him himself in that very dress which the poor man had received. After this vision the sainted man was not puffed up with human glory, but, acknowledging the goodness of God in what had been done, and being now of the age of twenty years, he hastened to receive baptism.
You can read more about St. Martin in Sulpicius Severus's Life of St. Martin.
UPDATE: Michael Gilleland gives us a Martinmas poem by John Clare.
UPDATE2: St. Martin of Tours and the Search for Holiness at "Ignatius Insight Scoop"