Thief
April 4, 2017
15:30
The good news: Gets turns frequently, steals extra items from enemies (Including some awesome ones at times), makes getting around the world map easier.  Congrats, you can steal the Genji Gear (Now just hope you roll a class that can use it)!  Fairly powerful once it can get the Twin Lance onwards.
The bad news: Very unimpressive in the first act.  Stealing can be a pain.  Most daggers are on the weak side. If you rolled them first life is going to suck.
Strength
+1
Agility
+16
Vitality
+2
Magic
-6
Hands
Daggers
Full Moon
Double Lance
Rising Sun
Armor
Medium Headgear
Medium Armor
Light Accessories
Command
!Steal
Abilities
Level
AP
Ability
Innate
Equip Stats
Description
1
10
Find Passages
Yes
Reveals the location of secret passages while exploring dungeons.  As you only need one copy of this to affect your entire party, equipping it manually is pointless (You should always have a thief under the FJF rules)
2
20
!Flee
Enables an immediate, successful escape from battle.
3
30
Sprint
Yes
Hold B to dash around the map.  Note that if you're on FFV Advance, you can have an accelerated movement speed by default - Dash will be overkill!  As you only need one copy of this to affect your entire party, equipping it manually is pointless (You should always have a thief under the FJF rules)
4
50
!Steal
No
Attempts to steal an item.  Has a 40% success rate - it then steals either the Common or Rare item (The chance of stealing the Rare item is 10/256 - or roughly 4%).  I'll try to list notable Steals below.
5
75
Vigilance
Yes
Prevents back attack.  Interestingly enough this even applies to battles with a normally 100% back attack rate; the one that comes to mind is the Jackanape.  As you only need one copy of this to affect your entire party, equipping it manually is pointless (You should always have a thief etc etc)
6
150
!Mug
No
Uses a normal attack, and then attempts a Steal automatically.  Note that Mug CANNOT activate "triggered effects" from weapons (Such as the Mage Masher's chance to cast Mute after attacking).  This can be bad OR good depending on the situation (can't have it reflected, the Chicken Knife's flee is disabled!).
  7
300
Artful Dodger
No
Speed (+16)
That's it. It might not sound like much, but if you aren't in the Natural Jobs challenge, this can actually be a lot.  This is the highest speed mod in the game and plays extremely well with normally slower classes or in concert with Haste (which then doubles the fill speed of the now mostly-filled-anyway ATB gauge).  If you don't need a specific active ability, a speed bonus shouldn't be underestimated!
Success Strategy
Get the best daggers you can and the specialised equipment and make full use of it.  It's about the only thing the Thief can do.  Also keep an eye on the Steal list, you can sometimes get access to certain equipment early this way.  Ensure that you do NOT miss the Twin Lance (Bal Castle Basement), as it's one of the most powerful weapons the thief can get and will last you until the Chicken Knife.
If you start out with four thieves, this is probably the hardest start.  Make sure to stock up on potions ASAP.  Get Dagger drops from skeletons in the Ship Graveyard to equip yourself fully, and steal Mithril Daggers in Walse Tower.  The extra boosts of power will help immensely.  If you're still not doing enough damage, the way your damage formula works, you should see a significant boost at around level 9-10.  Good luck.
Special Equipment
There's one accessory the thief will really want, and three near-unique weapons they can take advantage of (The Ninja can also use them)!  Remember also that the Thief's Mug command does NOT activate on-hit effects of the weapon, meaning should you pick up the Chicken Knife, the Thief can use it without ever fearing its 25% escape rate.
Gear
Attack Power
Where to find
Notes
Thief Glove
Act 1, Steamship.  Steal it from Sekmet (Act 3) or Necrophobia (Interdimensional Rift) if you missed it.  
Steal success rate doubles (40% -> 80%)!
Does NOT, unfortunately, affect rare steal chance ):
Full Moon
35
Act 1, Steamship or Lonka Ruins.
Deals full damage regardless of rows
Cannot be used with Double Grip, Magic Sword, or Thrown
Twin Lance
61
Act 2, Bal Castle Basement, Objet D'Art (Steal)
Act 2, Exdeath's Castle
Attacks twice
If you try to !Mug with Double Lance, it only hits once ):
Pretty sure this can't be used with Double Grip, Magic Sword, or Thrown
SNES/GBA: The double-damage property does not function with Actions from other classes (eg !Jump)
iOS: Actions from other classes DO deal damage twice when using this weapon (eg !Jump)
Rising Sun
71
Act 3, Solitary Island Temple
Deals full damage regardless of rows
Cannot be used with Double Grip, Magic Sword, or Thrown
Notable Steal List
Note: Almost every enemy in the game can drop common goods like potions, antidotes, etc.; a handful can drop Elixirs too.  Because there's so many of those, I'm going to restrict it to more interesting steals. Remember, the Rare Steals only have about a 4% chance of being obtained, and you can only steal once per enemy per battle.
Note 2: If you get lucky enough to have a Time Mage with you, the spell Reset will return the stolen items to enemies, allowing you to not have to completely reload the game when a steal fails.  Since rare vs common steal is determined only when you actually succeed, you can thus attempt multiple times for rare steals.
You can also get Reset via the Wonder Rod (see its section in the mechanics area)
There's plenty more steals than this - but these are some of the more important ones.  Many of these can also be obtained in other ways, but sometimes you can steal them earlier than you can find them.  Sorry I can't provide a better list; if you're playing Advance, check out every new enemy you defeat in the Bestiary and take a look at its goods.
Where
Who
What
Notes
Walse Tower
Wyvern
Mythril Dagger
VERY useful for 4x Thief parties
Near Karnak
Zu
Elixirs
They have no common steal so eventually you WILL get the Elixir
Steamship
Poltergeists
Hi-Potions
Normally not easily obtainable until Act 2
Karnak Escape
Gigas
Elixirs
Common steal, so it's easy to get them!
Crescent Island
Harvester
Silver Bows
Common steal, sells well!
Quicksand Desert
Sand Bear
Javelin
for Dragoons
Airship events
Crayclaw
Coral Sword
Electric sword, if you didn't stop by Jacole to buy one
Meteorite
Titan
Earth Hammer
for Berserkers, be ready to reset a lot to get it though
Ronka Ruins
Lamia
Lamia's Tiara
Headgear, especially valuable for Dancers
Exdeath's Castle (First visit)
Jail Bear
Spear
for Dragoons; weaker than all other weapons :/
Near Exdeath's Castle
Strapparer
Elixir
Only steal, so you'll get them eventually
Bal Castle Basement
Objet D'Art
Twin Lance
Amazing thief/ninja weapon.  Rare; common is Hi-pots
Drakenvale
Poison Eagle
Gale Bow
For Rangers
Xezat's Ship
Gilgamesh
Genji Gloves
Heavy accessory, also Paralysis/Frog immunity
Cave to northwest lake
Druid
Angel Ring
Immunity to Aging/Zombie
Barrier Tower
Red Dragon
Flame Ring
Absorb Fire, Immune to Ice, Weak to Water
Barrier Tower
Reflect Knight
Poison Axe
For Berserkers
Exdeath's Castle (Last visit)
Red Dragon
Flame Ring
See above
Exdeath's Castle (Last visit)
Owazoral
Mirage Vest
Armor that grants Image
Exdeath's Castle (Last visit)
Wall Mage
Wall Ring
Accessory with auto-reflect
Exdeath's Castle (Last visit)
Black Warlock
Judgment Staff
Holy damage weapon/casts Dispel on use
Exdeath's Castle (Last visit)
Gilgamesh
Genji Helm
Post-Morphing Time form only
Exdeath's Castle (Last visit)
Carbuncle
Wall Ring
Accessory with auto-reflect
Pyramid
Sehkmet
Thief Gloves
if missed at Steamship
Near Castle Bal
Mukare
Doom Axe
for Berserkers
Near Regole
Isteros
Judgment Staff
Holy damage staff/casts Dispel on use
Sea north of Mirage
Giant Bird
Murasame
for Samurai
Cave to Istory Falls
Druid
Angel Ring
Immunity to Aging/Zombie
Northern sea SW of Carwen
Stingray
Rune Blade
Sword that uses MP for extra damage
Solitary Island Temple
Owazoral
Mirage Vest
Armor that grants Image
Sunken Tower
Gogo
Gold Hairpin
Light Headgear that halves MP cost
Fork Tower
Omniscient
Kornago Gourd
for Beastmasters
Phoenix Tower
Bella Donna
Coral Ring
Absorb Water, Immune to Fire, Weak to Bolt
Phoenix Tower
Sol Cannon
Guard Ring
Auto-Regen
Phoenix Tower
Cherie
Red Shoes
for Dancer
Castle
Red Dragon
Flame Ring
Absorb Fire, Immune to Ice, Weak to Water
Castle
Bodyguard
Tempest
for Samurai
Castle
Fury
Cursed Ring
High stats, but start battle on 50 second Countdown
Castle
Jura Avis
Dragoon Spear
for Dragoons
Castle
Apocalypse
Giant Glove
High physical defense heavy accessory
Castle
Halicarnassus
Aegis Shield
Amazing shield
Castle
Twin Tania
Giant Axe
for Berserkers; must be stolen when Twin Tania is charging Giga Flare
Tower
AvisDragon
Artemis Bow
for Rangers
Void
Gorgimera
Aegis Shield
Amazing shield
Void
Necromancer
Bone Mail
!!!
Void
Crystal Dragon
Elixirs
common steal!
Void
Crystal Dragon
Dragoon Spear
for Dragoons; Rare Steal
Void
King Behemoth
Drain Sword
for Knights, if missed
Void
Gilgamesh
Genji Shield
During the fight at the start of the Void segment
Void
Gilgamesh
Genji Armor
When Gilgamesh appears during Necrophobia fight
Void
Necrophobia
Thief Gloves
if you've somehow missed them all this time
Void
Shinryu(!)
Dragon Whip
for Beastmasters; you CAN flee chest encounters to reset them!
Void
Neo Exdeath (Top)
Dragoon Spear
for Dragoons(*)
Void
Neo Exdeath (Front)
Tempest
for Samurai(*)
Void
Neo Exdeath (Back)
Ragnarok
for Knights(*)
(*) Those playing the GBA version can keep these after the credits roll!