Sky, you can find alot of that info at the site I linked
(this one) but I'll give you a quick (ha ha) overview..
(I've written names in English order btw)
Koji Kondo makes most of Nintendo's great music inlcuding the soundtrack for every major Mario game, and most of the Zelda games.
Hirokazu Tanaka created the music for DonkeyKong, Balloon Fight, and the original Metroid, among many others. He worked with
Keichi Suzuki on the Mother/Earthbound games.
Yasunori Mitsuda was Square's best composer (in my opinion that is) until he left to continue working with the Xeno team. He's famous of course, for Chrono Trigger and Chrono Cross.
Masaharu Iwata composed the beautiful soundtracks for most of the Ogrebattle/Tactics Ogre series, as well as FF Tactics. He seems to be credited for some work in Dracula X as well, but it could be another M. Iwata.
Hitoshi Sakimoto was his coconspirator for many years, and most recently worked on Breath of Fire V.
The Kukeiha Club is Konami's resident sound team (or was way back when). I have yet to hear a Konami ST I didn't like
Jun Ishikawa is responsible for the music in the Kirby series, excluding Dreamland 2 and the puzzle/ball games. A personal favorite, and heck, my name comes from the series... I had to bring it up.
Jun "Chiki" Chikuma gave us the beautimus, addictive sounds of almost every Bomberman game, as well as Do Re Mi Fantasy (play it if you can, great stuff), the original Adventure Island, and many other Hudson odds and ends.
I forgot to mention
Yoko Shimomura, who
should be known for Legend of Mana, Front Mission, Kingdom Hearts, Super Mario RPG, and a number of other non-FF Square games, in addition to Street Fighter 2 (along with
Alph Lyra, another grat composer to look out for)
Nobuo Uematsu is well loved by many, almost strictly due to the Final Fantasy series. I'll complain about that at least until Koji Kondo gets the same kind of worldwide recognition. To his credit, he's also worked on Gunhazard, Half-boiled Hero, and eight songs out of Chrono Trigger.
Yoko Kanno is known by some for the music in Napple Tale, Nobunga's Ambition, and Uncharted Waters. Her real talent wasn't shown until she broke into the Anime scene. With such credits as Escaflowne, Cowboy Bebop, Brain Powerd, Earth Girl Arjuna, and recently Ghost in the Shell: Stand Alone Complex, she deserves every bit of praise she gets. While most composers are only adept at one or two forms of music, Yoko seems to excel at any genre she tries her hand at. (yes, I'm a fanboy, but listen to her stuff and see if you can't sympathize)
oh geez.. I told you I could go on and on. of course, I'm looking up details as I go, but I know most of these names when I see them (and usually when I hear their music). I've also still neglected several important people, like the many talented composers at Sega (panzer dragoon anyone?), Zuntata (Taito's soundteam), and anyone outside of Japan (Chris Huelsbeck is cool, and Bobby Prince too). I'd list Capcom's greatest, but like Konami they have too many, and they're very hard to keep track of. I'll just try to remember Bun Bun, and Yuukichan's Papa.
I'm with ya Okiva. Amusement Vision has a great sound crew, much to the delight of F-Zero fans as well now.