Final Fantasy 3 Rare/Useful Items FAQ
Compiled by EdTheSaint with help from Lucid Flow
Version 1.2
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This FAQ basically lists ways to get very good items. Most of the ways can be done over and over, but there are a few that can't. A couple things I included aren't ways to get an item over and over or even an extra, but are just hidden. Most of the ways involve stealing and use of the colliseum, and a few need the Ragnarok esper. So, logically, you'd have to be in the WoR, with most of the characters, etc...
Just a little note...I'm not trying to take credit for any of this. I'm merely gathering this information and organizing it. Here are a few people that deserve to be thanked for contributing to the whole FF3 secrets and FAQs scene:
RabiteMan, Seriphosu, Mirrorstar, King Kung, JonN2002 and The Mynock (csmith@cps.cmich.edu)
All those except The Mynock are AOLers.
One last thing...there's no guarantee these will all work. I don't have time to try them all right now (I hope to do so in the near future). I've had people say certain things do work, and I've had other people say that the same method does not work. However, if something doesn't work for you right away, it may just be hard to do so don't give up. 
And now what you actually care about...
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Air Anchor:
1. In the Fanatic's Tower, search the wall right next to the chest in the 2nd room from the bottom of the tower. You'll hear a noise, and a door will appear on the floor below you. The location of the secret switch may be random for each game, I'm not sure. Nevertheless, it's in the Fanatic's Tower.
2. Bet Genji Armor at the colliseum.
AtmaWeapon:
Steal from Goddess, one of the statues in Kefka's Tower.
Cursed Ring:
1. Use Ragnarok esper on Veterans, Didalos (both in Kefka's tower), or SrBehemoths (fight them on the Veldt).
2. Killing Veterans and Didalos (Kefka's Tower) will give you one...eventually.
Cursed Shield:
Use Ragnarok esper on Didalos (Kefka's Tower)
DragoonBoots:
1. Steal from Wyverns (in the WoB or on the Veldt)
2. Buy 'em in Tzen for 9000GP (only shop that sells them)
DragonHorn:
Get BehemothSuits by fighting SrBehemoths on the Veldt, and get at the colliseum. Keep betting until you get a DragoonHorn
Economizer:
1. Kill Brachosaurs in the forest north-west of the Veldt. Try using Vanish/Doom if you can't beat them...they may sneeze you away before you can kill them or use Ultima which'll probably kill you.
2. Steal from Aquilas (found in Phoenix Cave)
Exp. Egg:
Fight Tyranosaurs in the forest north-west of the Veldt, and you'll occasionally win Imp Halberds. Bet these at the colliseum, and keep betting what you win, like this:
Imp Halberd -> Cat Hood -> Merit Award -> Rename Card -> Marvel Shoes -> Tintinabar -> Exp. Egg -> Tintinabar
Obviously, this is also a way to get as many as you like of the items in between.
Gem Box:
Use Ragnarok esper on Boxed Sets (found in Ancient Castle). No one I've talked to personally can confirm this...I think I may try it myself to make sure. Apparently, though, I've found people who easily turn them into items with Ragnarok, but occasionally it will miss. I think when it misses...that's when it's trying to get the Gem Box but can't.
Genji Armor:
Steal from Vindrs, Wild Cats, Soul Dancers, and Dahlings in Owzer's House. They'll give you either a Tabby Suit, Chocobo Suit, or Moogle Suit. Take any of these to the colliseum, and keep betting what you win, and you'll eventually get a Genji Armor.
Genji Gloves:
1. Steal from Dragons (found on the Floating Continent, or the Veldt in the WoR).
2. You can get one early on in the game by saying "no" the first time when Banon asks Terra if she'll be their last ray of hope. After you say no, talk to everyone in the Returners hideout and someone will try to "persuade" you with it to join them.
Genji Shield:
Bet ThunderShlds at colliseum. You can get ThunderShlds by either stealing them from Steriodites in Kefka's Tower, or by betting Genji Gloves and the colliseum(see section on Genji Gloves).
Imp Armor:
Steal from Tyranosaurs
Imp Halberd:
Win from Tyranosaurs in the forest north-west of the Veldt.
Megalixer:
1. Steal from Earthguards in the desert of the Solitary Island (Peepers will give you regular Elixers...not bad).
2. Steal from Kefka (Steal immediatly when the fight begins...and use it after Kefka does Fallen One).
3. Use Ragnarok esper on Intangir (fight them on the Veldt).
Moogle Charm:
Go back to the cave in Narsh where you got Mog in the WoR. Search by pressing A up against the wall where he used to be standing.
Muscle Belts:
Steal from Borras, found on Mt. Zozo.
Offering:
Use Ragnarok esper on Samuri (found in Ancient Castle or Train in Cyan's dream).
Ragnarok Sword:
Steal from Doom, one of the statues in Kefka's Tower.
Red Jacket:
Buy Ninja Stars at Thamasa, and keep betting at the colliseum like this:
Ninja Star -> Tack Star -> Rising Sun -> Bone Club -> Red Jacket
I think Red Jacket is the strongest armor for Sabin and maybe some others. This is also just a great way to get Tacks Stars, Rising Suns, and maybe a Bone Club if you wanted one.
Relic Ring:
Use the Ragnarok Esper on SrBehemoth.
Ribbon:
1. Steal from Brachosaurs in the forst north-west of the Veldt.
2. Use Ragnarok esper on Dahlings, Barb-es, L.80 Magics, or L.90 Magics.
3. In Locke's scenario, use the Old Clock-Key and go through the passage behind the chest. Then go through the hall way untill you come to a path that branches off to the right (the right side of the screen...since your character is facing down, it would be his left). Follow the path that branches off until you reach a point where there are 4 ways to go. The downward path is covered by the ceiling, but you can still walk down. Walk down, while occasionally pressing to the left. You'll find a hidden path off to the left...but there is another one that goes down. If you go down this path you'll come to a stairway.
Safety Bit:
1. Use Ragnarok esper on Woolly
2. Steal from Doom, a Statue in Kefka's Tower.
Snow Muffler:
Beat SrBehemoth's on the veldt and you'll win a BehemothSuit. Bet it at the colliseum to get a Snow Muffler.
Tintinabar:
1. Use Ragnarok Esper on Spek-Tor.
2. See Exp. Egg section...
3. To get a Tintinabar Early in the game, during Sabins scenario, in the town on the Veldt, there will be a wounded soldier in one of the houses.. Keep reading him letters from Lola and after, keep sendind letters to Lola. Eveuntually, he will give you a tintinabar.
Titanium:
Bet Tortoise Shield at colliseum.
Tortoise Shield:
Bet Imp Armor at colliseum.
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Other stuff you should know:
If you are trying to steal or use Ragnarok on an enemy, be warned that most enemies can have 2 or 3 items you will get. The one you want may be harder to get than others. For example, that's why using Ragnarok on SrBehemoths may give you Cursed Ring, or it may give you a Relic Ring.
The Atma Weapon's power is based on how much HP you have. It's weak in the beginning of the game, right when you first get one, but I think when the user has around 6000 HP it starts getting strong (it'll take 9999 every time). 
The Cursed Shield will turn to the Paladin Shield after using it for around 255 battles. If you didn't know this already you must be some kind of hermit. Of course, the Paladin Shield has amazing godlike power and everyone can take one, so they're really good to have. Essentially, every Cursed Shield you get is a Paladin Shield. In case you're new to the internet or something and havn't already heard this 10,000 times already, equip the Ribbon and most of the effects of the Cursed stuff will be nullified. I suggest you take a party of one person (who will be equipped with the Cursed Shield, Cursed Ring (if you have one), and a Ribbon) to the Solitary Island. The enemies there will kill themselves. Now all you need is patience.
The Cursed Ring will turn to a Hero Ring when dispelled (do the same way as the Cursed Shield). Not too hot, considering you can buy those at the auction house.
I think the higher Locke or Gogo's speed is (look at their status screens), the more likely th