Palom - I don't like either of the twins, nor do I like Twincast.
Porom - See above.
FuSoYa - Glorious hairline and spell list; not much else.
Edward - I like the wandering prince-bard idea, and the waterhag fight.
Yang - I love his map sprite, and I hit him with a frying pan. <3
Kain - He's a solid fighter, and that's all I really need from him.
Rosa - I like her and Cecil as a couple, and she's pretty determined to follow you wherever you go. Spaaaaaaaaaaaaaaaaaaaaaaaace!
Rydia - One of my favorite summoners in the series.
Tellah - I love cranky old people that hit people with sticks.
Cecil - He's kind of bland, but I like him all the same, and he's one of the most reliable members of the party combatwise.
Cid - Cid-KO2.gif
Edge - Ninjas are traditionally my favorite class in the series, and Edge is a decent enough throw machine. That can steal. And has elemental magic because. I also appreciate the story bit with his parents, even if I don't think it has the weight it should for whatever reason. Oh, and the airship repair scene where he starts flirting with Rydia and Cid drags him away is probably my favorite in the game.