Unlock Sound Test
Beat Final Fantasy 1 and 2 once to unlock a sound test.
FF1 Mini Game
While on the ship, hold down A and keep tapping B. Soon, a sliding tile minigame will appear. The aim of the game is to put the numbered tiles in order from 1 to 15. If you do well, you gain items and money.
Here lies Link
In Final Fantasy I when you visit Elfheim, press A on the left most tombstone behind the inn. It will say "Here lies Link." Link being the famous elf star of the Legend of Zelda series.
Tile Game
In FF II there is a match-the-faces tile game that gives items and cash prizes. When you are on the ice sled, hold A and keep pressing B to bring up the game.