Nobuo Uematsu, who has been working at Square (SquareEnix) for nearly twenty years, is the composer behind the music from Final Fantasies 1 - 9. He also composed parts of the Saga series soundtrack, some of the Chrono Trigger music (though Yasunori Mitsuda did most of it), and a couple of the tracks in FFX.
He now has his own band, the Black Mages, who perform rock arrangements of Uematsu's music. Also, www.ocremix.org and various videogame remix projects have done arrangements of his work.
Nobuo Uematsu plans to retire from Squeenix this year, but he will always be widely regarded as one of the best videogame music composers.
Nobuo Uematsu is the veteran composer at Squeenix.