There used to be a huge market in Europe and the Middle East for relics allegedly associated with Jesus Christ. Pieces of the "true cross" probably added up to a cross the size of a redwood tree. (While not directly related, it's an interesting note that Dr. Karl Shuker, a cryptozoologist, has traced venerated feathers from "angels' wings" to early specimens of birds of paradise, whose feathers seemed exotic indeed to Europeans. This in turn reminds me of the divine joke played in Holly Hunter's series "Saving Grace," where Grace plucks a feather from the wings of her angel, Earl, and takes it to a lab only to learn it's become a common pigeon feather.)
Anyway, to get back on topic...
The Catholic Church in the last century has been careful to distance itself from all but a fraction of relic claims. The Church even permitted removal of samples from the Shroud of Turin to carbon-date it.
Still, claims of new relics - at one point, even the burial box, or ossuary, of Jesus - still appear. The latest is a claim made in a film that two iron nails found in the tomb of Caiphas, the high priest who condemned Jesus, were buried with him because they came from the cross of Jesus.
While such iron nails were used in crucifixions, the claim is shaky. Israeli authorities say this particular tomb's link to Caiphas has never been proven. Even if it was his tomb, why exactly would nails from Jesus' crucifixion have been placed in it? To celebrate his role in the event or to mock it? And if Jesus' followers had retrieved the nails somehow, would they not have kept them instead of letting them be buried?
As A Christian, I believe that something unique and amazing occurred after this troublesome traveling preacher was executed. But clear thinking requires us to be very cautious about claims of relics.
FOLLOWUP - An interesting article in a Catholic periodical says that the normal idea of tons of "True Cross" wood isn't true: all the claimed relics we know of would, if somehow glued back together, make a piece smaller than the crossbeam Jesus carried. (The uprights for crosses were maintained "on-site" in a standing position - condemned men carried only the crossbeam.) The Church does say that many claimed relics of the cross are fake, but those maintained in churches in Rome and Jerusalem are most likely authentic.