Of course we are not talking about a simple crucifix 
I have to point this out: A
cross and a
crucifix are not the same thing, and the distinction is quiet important in art.
A cross is just two bars crossed, without any specific form other than that. For example this: x is techniquelly also a cross. In a religious, christian context, it is usually one slightly longer vertical bar and a slightly shorter horizontal bar. I think some orthodox churches use a symetrical cross, but I'm not sure.
A crucifix, on the other hand, is a representation of the cruxification of Jesus. That is, a crucifix always includes a cross on the one hand and a figure of Jesus on the other, be it as a statue or just an image. Sometimes, there's a plate with the inscription INRI on a crucifix, which stands for Jesus of Nazareth, King of the Jews, in latin.
Sorry, this is a bit of a pet peeve of mine - and I also wanted to clarify: Is your question about a cross or a crucifix?
As for carpenter nails, I know that many churches claim to own some of the nails that were used to nail Jesus to the cross. So I assume it's possible that some other churches also use more modern carpenter nails to remember this.
Edit: Then there's the Cross of Coventry. I can't remember the details, but after the destruction of the whole city in WWII a cross was made out of some of the debris - probably carpenter nails, considering your question (if I'm right, of course), and copies(?) sent all over the world, most likely among others to Dresden, which was also destroyed in the war - and is now partner city or something of Coventry. I don't know anything about an inscription, but maybe "Coventry"? These crosses are meant to promote peace.
