This article is from the Final-Fantasy and other Square Soft Games FAQ, by firstname.lastname@example.org (Nick Zitzmann) with numerous contributions by others.
Knight [L2 Squire]
Early in the game, knights are useful as military units. They can break
the equipment of other characters, which is sometimes useful in
disabling human opponents. However, there are better physical jobs out
Archer [L2 Squire]
Archers are the only characters in the game that can be equipped with
bows. Having a long range attack is useful by itself, but the archer is
especially useful when he/she is located higher than the target. The
Charge skills aren't that useful, but the Concentrate ability is.
Monk [L2 Knight]
Monks can pound enemies for huge amounts of damage, and they aren't even
equipped with weapons. The Punch Art and Counter abilities are also
Priest [L2 Chemist]
Priests are the White Wizards of previous Final Fantasy games. They can
use white magic spells, but none of them (except for Holy) are all that
Wizard [L2 Chemist]
Wizards are the Black Wizards of previous Final Fantasy games. They can
use black magic spells, but later in the game, only the costlier spells
will be useful. They're useful when the spells are cheap, at the
beginning of the game, but are difficult to maintain afterward.
Time Mage [L2 Wizard]
Time Mages provide easy ways to drive your competition crazy - they can
speed up characters, slow/stop them, and cast the mighty Meteo spell.
Worse yet, the computer can usually make very effective use of them.
Nevertheless, it wouldn't hurt to have some characters with time magic
Summoner [L2 Time Mage]
Summon spells are not only visually impressive, but in a few ways,
they're the most powerful type of magic that can be cast. Summon spells
affect an entire area instead of five squares, and typically deal out
big damage. However, spells take a lot of JP to earn.
Thief [L2 Archer]
Thieves can steal stuff from enemies, but tend to be killed very easily
because of their low armor. Draw your own conclusions.
Mediator [L2 Oracle]
Mediators have abilities no other class can perform: Their Talk Skill
can increase/decrease the bravery/faith of any character, and their
Invitation skill can invite any normal enemy into the party. They can
also use guns, which adds a little to their value.
Oracle (Yin-Yang Mage) [L2 Priest]
Yin-Yang Magic can change the status of the enemy, but it adds more
insult than injury. As a result, this class is rather useless. Temple
Knights are more useful, and perform the same general actions.
Geomancer [L3 Monk]
Geomancers can equip most of the same equipment as knights and squires,
and can use the elements to assault the enemies. However, since the
magic is rather weak and never improves, it's only useful at the
beginning of the game.
Lancer (Dragoon) [L3 Thief]
The Highwind family would be proud of these guys. Jump attacks increase
the power of regular attacks, and once a lancer is in the air, they
can't be attacked until they come back down. This job is one of the best
attack jobs to acquire.