Ninja. I HAVE to pick the Ninja, for a mulititude of reasons:
Throw. Combine with the Fire/Ice/Lit items (Fire Tech,etc. on the ROM). Whoop any monster group.
2-Swords. Combine with Mime and Monk Mastery. Whoop any single monster.
2nd Highest Speed bonus for Job Mastery. Thief who?
Also, since Speed is so high, a Ninja will almost always go first. Remember that little Throw command?
Coolness factor. Maybe not as cool as Dragoons, but close.

I could go on, but I think you get the idea.

2nd place is a tie between Dragoons (coolness factor, Butz as a Dragoon looks just like *sees The Man glaring at him*... well, uh, just go look!) and Monks (Counter, Best Vigor and Stamina, don't need weapons, attack twice).