The following characters are listed in the chronological order in which they were controllable outside of battle:
ZIDANE (story prologue on the Prima Vista), VIVI (in Alexandria before the play), STEINER (assembling the Knights of Pluto), QUINA (catching frogs in Qu's Marsh), GARNET (escaping Lindblum with Steiner through South Gate), FREYA (in Cleyra), CID (as a Frog in the Desert Palace), and EIKO (navigating the Desert Palace).
AMARANT is a main character who remains with the traveling party through the course of the entire game, but is never controlled by the player outside of battle. BEATRIX tails Steiner when defending Alexandria from Kuja's attack, and follows the player's input in battle, but is never controllable outside of battle. MARCUS, CINNA, and BLANK are all playable characters at one point or another in combat (especially Marcus), but none assume control of the party outside of battle.
If one wanted to get technical, any time a vessel is being piloted that can be controlled by the player, it is assumed that whomever at the wheel is actually being controlled (and not the vessel itself, which is all the player can see). Examples include the aforementioned Blank (piloting the Blue Narciss), and Erin (piloting Hilda Garde 2 and 3).