Isn't this in the FAQ?

When FFVI was released in Japan, Square knew right away they wanted to release it in America. However, only two FF games had been released in America at this point (FFI and FFIV, which was released as FFII). Because of this, Square released FFVI in America as FFIII. When Square jumped ship to the Playstation, they started giving the games their proper title. When FFVI was re-released for PS1, it was numbered correctly. The actual FFIII has not yet been released in the US, but it is slated to be re-released on the Nintendo DS.

Handy dandy release comparison chart:

Japanese --------- US
Final Fantasy ----Final Fantasy (Famicom/NES)
Final Fantasy II --Not released (Famicom)
Final Fantasy III --Not released (Famicom)
Final Fantasy IV --Final Fantasy II (Super Famicom/SNES)
Final Fantasy V ---Not released (Super Famicom)
Final Fantasy VI --Final Fantasy III (Super Famicom/SNES)
Final Fantasy VII --Final Fantasy VII (Playstation)

Final Fantasy V
Final Fantasy VI --Both released in Final Fantasy Anthology (Playstation)
Final Fantasy IV --Released in Final Fantasy Chronicles