Following the release of the original Final Fantasy, America didn't get another one until Final Fantasy IV (which was marketed as FFII). This game was watered down badly, since it was considered all we American gamers could handle. Final Fantasy V was also exclusive to Japan, so when FFVI was released in the US, it was called FFIII. When FFVII was released, the correct numbering system had been restored.

Over the past few years, several PS1 FF collections have been released. FF Anthology, the first, contained FFV and FFVI (numbering system restored, obviously). FF Chronicles had FFIV (difficulty restored, censoring removed) and Chrono Trigger. FF Origins had FFI and FFII (actual FFII, not FFIV). As such, the true FFIII is the only FF that hasn't been released here.

However, FFIII will be released on the Nintendo DS. Hence, the "not released in the United States" designation will soon become obsolete.