The first ever Final Fantasy game was released in Japan in 1987 and North America in 1990. The Famicom/NES release of Final Fantasy was when Squaresoft really made the rest of the world first sit up and take notice.

Final Fantasy got an English language American release, in 1990, and JRPGs were becoming more popular in the West. In part due to games such as this, and Enix‘s Dragon Quest series.

This Famicom/Nintendo Entertainment System release, though, is really where the core of the next decade of Final Fantasy games were seeded.

Thank you to Zeke for clarification of the release dates.

More: Final Fantasy on Wikipedia