Tina Best character in the game. Her ability to change shape combined with the right equipment makes her ultra-powerful.
Locke Locke is alright. Some people say that he potentially the most powerful character in the game, but I only found him to be ok. Might be worth using him to steal items from bosses.
Edgar: Edgar is a good fighter, and he stays a good fighter. Useful through the game
Sabin Another good fighter. I found him to be better than Edgar early game, while Edgar inches out later on.
Shadow Failed to save him, so I don't know
Cyan Cyan looks like he might be a stellar character, but he is quite bad. Why? Well, his special ability takes so much time to prepare that by the time any of the more powerful moves are ready, you would have been able to attack several times with your other characters, which would have been more useful.
Celes Celes is similar to Terra in her use, and while she is worse late-game, her ability to block magic still makes her quite useful. You just need to make sure that you don't block your own spells.
Gau Too random to be good. Sometimes he will do well, quite often he won't. I did not like him.
Gogo Hard to find. Gogo can be used for some cheesy moves, and at some points in the game he is useful, but I found more annoying than anything else.
Umaro Too random. I found him to be good at exactly one place in the game, and at best tolerable at others.
Relm Best magic stats in the game makes her useful. Can be a bit annoying to use as she is squishy, but she is one of those characters that will shine late-game (though not because of her special move)
Stratgo Blue mage. Might be good, but I've always found blue mages too annoying to be worth the time, so i can't comment on him.
Setzer Another random character. He "might" be very powerful, but there is also a big chance that he'll be useless. Can be upgraded with a skill that makes him throw money instead of using his random skill, but it does not deal enough damage to be good.
Mog Ugh, why did they feel the need to have so many random character? Mog is too unreliable to be good. Dance is also dependent on where you are, and using a dance for an area that you are not in has a relatively high fail-chance, but enemies will often have some resistance against their "local" element.