oenone's writeup on Valentine's Day contains all the biographical information on Saint Valentine that one would need, so I won't repeat it.
Saint Valentine's remains are currently held in several different places. A small Carmelite church on Whitefriar Street in Dublin, Ireland currently claims to have the greater part of Valentine's remains, which were sent from Rome in 1835 as a personal gift from Pope Gregory XVI. Pope Gregory also included a letter which the monks have faithfully retained, proving the authenticity of their claim. However, either out of respect or out of fear of what might be in there, the lead casket containing the relics has never been opened. One of the monks said, "The letter we have tells that the casket contains the body of St Valentine but it doesn't go into any more details than that. We are not told that we have the entire body and everything there is with it."
Apparently Saint Valentine's heart may be in Scotland, and certain other body parts may be in his home town in Italy, and in fact many sources on the web state that "most" of his remains are in fact in the Church of St. Praxedes in Rome, which suggests that perhaps Pope Gregory pulled a fast one on the Carmelites. However, the truth may never be known, and every February 14th the casket is brought out to a special place on the altar and the church becomes crowded with religious couples who have turned up to have their wedding or engagement rings blessed.
Today one of the backbenchers in the Dail (the Irish parliament), Martin Brady, suggested that Ireland should exploit the tourist potential of Saint Valentine's remains more, perhaps having seen the hysteria that surrounded the passage of Saint Therese of Lisieux's relics around the country, in which hordes of old women trampled each other in attempts to touch the casket of her bones. Mr Brady said the Dublin could "rival Paris as one of the top cities for love," and suggested that the tourist authorities create "trails of romance" marked by pink heart-shaped signposts at significant spots. The wholesale prostitution and Barneyfication of Ireland's once-authentic religious and cultural heritage shows no signs of slowing down.