Typically a black market sells items that are either obtained illegally, or illegal themselves. I suppose there could be certain useful items that aren't allowed to be sold in cities that you could sell outside of the AH, but I don't think it would really feel like a black market since the game clearly allows you to obtain and sell them. It would just turn out to be an annoyance to players.
RMT is a black market, as well as selling accounts. These two will inevitably occur in FFXIV, but I doubt you'll want to take part in those markets.
"It's a magical world, Hobbes ol' buddy. Lets go exploring."
Just for clarification, I bot, sell gil, buy gil, MPK, party naked through the dunes, power level, play as a Ranger, quit when they nerf it and complain, play as a Beastmaster, quit when then nerf it and complain, make posts for and against RMT, monopolize NMs, create elitist groups, run casinos, steal gil, hack accounts, and stare at you awkwardly with my left eye.