Dyes are purely cosmetic. However, they should always be sold to the dye trader (or other players if they offer more than the dye trader), instead of the normal merchant. Black is scarcer than the rest, therefore you can sell them for more. And it has some l33t value for people who want to look mean, pushing up the price.
I once sold a green bow that was apparently worth about 45K at the time, to the merchant from 125 gold, before I knew what green items were. I guess that is how one learns. Sigh.