Final Fantasy III:
Send seven mails to another player using Mog Net. Then, send four mails through Mog Net to the NPC "The 4 Old Men", and another four mails to "King Alus". It does not matter what order this is done, as long as Alus is last. After reading the fourth one you will unlock the new dungeon. Ride on the Nautulus and go east of the floating continent. Once there you will see a shadow in the water. Go underwater and move into the coral to enter a cave. There is no real dungeon here, but there is a difficult Boss, Iron Giant.
Register someone multiple communication IDs on Mog Net. Send seven messages to another player. Send and receive four messages from Topapa. After reading the fourth one, you will get a message giving you a mini-quest. Go to Uoul and talk to Topapa. Go to the cave that is to the north of the other cave. Enter, then defeat the three Bombs to get a piece of crystal. This will unlock the Onion Knight as a job.
If you get the Onion Knight, there are special weapons and armor that only he can equip. They are called the Onion Sword, Shield, Gauntlets, Helm, etc. You can get them by fighting red and green dragons. These can be found towards the top of the Crystal Tower and in the "secret dungeon".
This trick works on any item you can use in battle, such as Elixirs or Phoenix Downs. Enter the item menu outside of battle. Move the item to be duplicated to the first slot. While in battle, choose the item menu, then press Up + A. If done correctly, you should see a flash of the equipment screen before seeing the main menu again. Press B to cancel. The item is now duplicated. You can repeat this as many times as desired, but be careful not to get more than 99 of an item as it may glitch your game or saved game file. Note: Items can be in either the top left or top right hand corner to be duplicated.
Choose a high-priced item to sell, then use the "Item duplication" trick. Sell all of them except one, then repeat as many times as desired.
Go to the Town Of The Ancients and talk to the child two stories up the grass hills. He is back behind the stairs. He will tell you that he will give you a prize if you ride around the continent. Leave town and go east a bit. Get a Chocobo and ride around the outside of the continent. Go back and talk to the child to get your rewards. Sell them, then repeat.
After you are dropped out of the dragon's nest, go to the area with the spring and the gnome. Talk to him, and he will give you a Mini. However, you can talk to him again and get one for all of your party members.
You can use certain items instead of spells if you run out of MP. For example, if your Black Mage wants to use Fire but is out of MP, go to the item screen and use the item Fire Staff. This seems to only work if your character is able to equip the item that is being used. Also, not all items work. Items that work include the Ice Staff, Fire Staff, Light Staff, and Salamd Sword.