There were characters that followed your party around for plot purposes. You could talk to them with the B button, but other than that, they were useless. I've always thought that, in the event of a remake, this should be changed; I think it'd be great if, at the beginning of every battle, you'd have a chance at getting a certain effect depending on who your current "support" character is. Like how the Invincible fires that cannon at the beginning of each fight, except it would occur more seldomly. Sarah could do some healing/Esuna-like thing, Cid could call in an air raid or something, Desh could summon one of those Baby Bahamuts, Elia could provide some more healing or summon a tidal wave, Allus could extort extra Gil from monsters, Dorga could let loose with that mad sagacious magic, and Unne could inflict some status ailments on enemies--Sleep at the very least.

Square Enix probably won't want to mess with the game quite that much, though.