For years, no, decades, a legend has sprung up around the title Final Fantasy. It says that Square, which was in dire straits, thought this was going to be its last game -- hence, Final Fantasy. The game's creator, Hironobu Sakaguchi, says that myth is wrong.
As reported by Famitsu (via Game Kana), Sakaguchi recently gave a talk about the history of JRPGs. According to Sakaguchi, the original idea was to give the game a title that could be abbreviated to "FF" in English (in Japanese, that is pronounced as "efu efu"). It's a nice sounding abbreviation to Japanese ears.
The word "fantasy" in Final Fantasy has always made sense. These games are fantasy. But the word "final" has always been a sticking point for some players. The legend surrounding the game's name, however, explains why "final" is used.
However, the original title was going to be Fighting Fantasy. At that same time, there was board game by the same name. (Here, I'm assuming Famitsu is referring to the single-player Fighting Fantasy roleplaying books, which spawned board games.) Because of this, the title was changed to Final Fantasy.
"Final" (ファイナル or "fainaru") is a famous word in Japan, so for the game's creators, it was probably a logical "F" word to pick.
So what does Sakaguchi say to the notion that this was conceived as the company's final project? "Those days definitely seemed like end times, but honestly, any word that started with 'F' would have been fine."
So... Fabulous Fantasy? Fearless Fantasy? Fluffy Fantasy? Nah, glad they went with "final," even if Square Enix keeps pumping them out.
Actually, wait. Is it too late to change the name to Forever Fantasy?