FFL1 - Nobuo Uematsu
FFL2 - Uematsu and Kenji Ito
FFL3 - Ryuji Sasai and Chihiro Fujioka (4 songs only)
RS1 - Ito and Uematsu (1 song only)
RS2 - Ito and Uemsatsu (2 songs only)
RS3 - Ito
SF1 - Ito
SF2 - Masashi Hamauzu
U.SaGa - Hamauzu
Uematsu is famous for of course, the Final Fantasy Series. He’s done a few other older NES games for Square, and he also started off the SaGa series.
Ito is known best for composing the majority of the SaGa games 4 1/2 games. He also composed the Bastard Child of the SaGa series, WildCard, for WSC I believe. Other than that, his other more famous works include the First Seiken Densetsu game, and a DC RPG called Culdcept 2.
Ryuji Sasai is a Squaresoft composer who has only done a few games. The only games I know that he has composed in are FFL3 (the majority of it), Rudra No Hihou, and he co-composed Final Fantasy Mystic Quest. He also did a few songs for a Squaresoft fighting game (?) called Tobal No. 1.
Chihiro Fujioka is the co-composer of FFL3. Only 4 songs. The Submarine theme, the Game over theme, the Uh-Oh theme, and the Ending. His/Her style is orchestral, and fairly well done from what I can tell. My best guesses are that he was not a VG Music composer, and probly scored movies. Either that or he’s a sound designer and not really big on composing. This happens: Yukio Nakajima, who composed the Lufias on GBC and GBA, is not a composer. The only thing is, in his case, it really shows. 
Masashi Hamauzu didn’t really do much before the SaGa games. The only other works of his that I know of are a few tracks on Front Mission: Gun Hazard, and some co-composition in Final Fantasy 10 which were pretty nice.