The Cast
FF VI involves a large group of heroes who's stories develop in great detail throughout the course of the game.  I've placed the names from the Japanese version in parenthases where aplicable.
Terra (Tina) Branford:  Born of a mysterious past of which she can remember nothing, Terra is forced against her will to fight for the Empire.  After a failed attempt to collect a frozen Esper from the mines of Narshe frees her from her slave crown, Terra must decide whether she will continue to fight in the escalating war for the rule of the world.
Locke (Lock) Cole:  Locke is a treasure hunter extrordinaire.  He's traveled the world collecting valuable and rare artifacts, through whatever means neccessary.  He's got a major complex about protecting women, due to events in his past.  He is also a member of the Returners, an organization that is rebelling against the Empire.
Edgar Roni Figaro:  Edgar is the king of Figaro.  His castle is built right in the middle of a huge desert, much to the chagrin of anyone having to visit him.  He tends to be a bit on the womanizing side at times, but he really is a gentleman at heart.  Though Figaro is allied with the Empire, Edgar has secretly joined the Returners.
Sabin (Mash) Rene Figaro:  Edgar's twin brother who gave up all stake in the throne to be free of the pressures of ruling a kingdom.  He left Figaro Castle in order to train in the martial arts and become a disciplined fighter.  Sabin has been watching the current events from afar, but has finally decided that the Empire has gone too far and must be stopped.
General Celes Chere:  Having been infused with magical powers when she was just a child, Celes was once one of the most powerful generals in the Empire's army.  However, she has a moment of conscience and she is labled a traitor.  The Empire has her locked away in South Figaro, where a certain treasure hunter rescues her.
Shadow:  A mercenary for hire, Shadow will do anything for the right price.  He has concealed his past and killed his emotions.  His only companion in the world is his faithful dog, Interceptor.  Shadow trusts no one but himself.  He may leave your party whenever he feels like it, so don't feel too attached to him.
Cyan (Cayenne) Garamonde:  Cyan was the faithful retainer to the King of Doma, until Kefka and the Empire poison everyone in the castle.  The King dies, but worse for the swordsman, Cyan's wife and child also perish.  He has a difficult time letting go of the past and moving on with his life.
Gau:  After his mother died giving birth to him, Gau's father had a complete breakdown and took Gau into the wilderness, cursing him as a demon.  Gau has lived his entire life with the monsters on the Veldt.  He has learned to survive on his own, yet he enjoys the companionship he finds when he joins up with Cyan and Sabin.
Setzer Gabianni:  Setzer is the ultimate free spirit.  He lives his life on his airship, the Blackjack, gambling and living the high life.  He believes in taking risks, and plenty of them.  He will bet on anything if he thinks he might win.  In my opinion, Setzer has the best line in the entire game (and it's full of good lines), "My life is a chip in your pile.  Ante up!"
Strago (Stragus) Magus:  Strago lives in the town of Thamasa, the last settlement of the heirs of the Mage Knights of the War of the Magi, 1000 years before.  Though the powers of the descendents of the original magical humans have diminished, Strago is still quite adept at using magic. 
Relm Arrowny:  Relm is the "granddaughter" of Strago.  She is an aspiring artist, and loves to paint everything.  She develops a strong bond with Interceptor when the group enters Thamasa to investigate Espers.  Even though she's just a child, she can be a terror.  She is constantly taunting and tormenting Strago, though deep down she loves him more than anything else.
Mog:  Mog is one of the moogles of Narshe.  He is the only moogle that can speak to humans.  He claims that Ramuh came to him in a dream and told him to wait for the intrepid adventurers and join them. 
Umaro:  Umaro is a Yeti that lives in the mines of Narshe.  He is incredibly strong, and no one can control him.  Unless of course it's that little moogle, Mog. 
Gogo:  Gogo is a complete enigma.  Under all of the elaborate and thick clothing this being wears, no one can tell if Gogo is a man or a woman.  Gogo's origins are a mystery, and it is never explained as to who or what Gogo is.
The guy you love to hate
Kefka.  There's no other villain like him.  Unless you count Sephiroth.  Or Golbez.  Or, well, you get the point.  And yet Kefka is so much more than a psycho hell-bent on dominating the world and becoming some kind of deity.  Kefka is one of the places I think that Nobuo Uematsu outdid himself when writing the character themes.  The music for Kefka starts out small, and eventually rises into a crescendo of madness.  Kefka's determination to destroy every living thing and his hatred of anyone who experiences happiness, along with his light sense of humor make him one of the greatest villians in the history of video games.  He may not get the attention Sephiroth gets, but he is definately one of the most evil characters in any video game, and probably the most enjoyable to hate.
Peripheral Characters
One of the good things about FF VI is that there is so much interaction with NPCs.  Listed below are some of them, mostly my favorites.
General Leo:  The third general of the Empire at the outset of the game along with Kefka and Celes.  General Leo is a soldier driven by chivalry and the proper conduct of war.  He helps the party in the search for the Espers, only to be double crossed and killed by Kefka.  After Leo's death, Cyan (who has such a deep seated hatered for the Empire and anyone associated with it) makes the comment that he was their best soldier.
Bannon:  Though Bannon is a playable character for a short period in the game, he is still considered by most players just a peripheral character.  He is the leader of the Returners and helps Terra to finally come to her decision about the Empire (by bribing her, but things worked out for the best).  After the Espers attack Vector, Bannon is not seen again, mostly because the Empire is destroyed and the Returners aren't a strong enough organization to face Kefka in his god-like form.
Duncan:  Sabin's instructor in the martial arts.  Let's face it, anyone who can train Sabin to be that much of a badass has to be ubernasty.
Lone Wolf:  A pickpocket in Narshe, he takes all the treasure from the locked room. 
Impressario:  Not to be confused with the guy on the Phantom Train, this Impressario runs the opera house south of Jidoor.
Siegfreid:  This guy pops up in a couple different places, taking treasure away from you and pocketing it.
Hosted by www.Geocities.ws

1