2000 free coins
In chapter 5, enter the tunnel between Branca and Endor. Go through the tunnel and up the stairs on the other side. Re-enter the tunnel, and go up the stairs on the other side. Keep doing this and eventually you'll get 2000 free coins to use in the casino! But you can only do this trick once, I think.
Always inflict critical hits in boss battles
This weird glitch only works in the Japanese version of the game. When you're fighting any boss, choose to escape 8 times. Each time will fail, but if you do this procedure, for the remainder of the battle your physical attacks will always be critical hits! It doesn't matter what you do in between the failed escape attempts; you ARE allowed to do other things (such as cast spells) in between each escape attempt, but be sure you can survive getting attacked freely for each escape attempt.
Casino Price Overflow (Japan-only)
If you try buying a number of casino coins in Dragon Quest IV that would exceed the value of 16,777,215, then the price will essentially wrap around, i.e. the price you pay will become the remainder of the actual price divided by 16,777,216. This is most well known for permitting you to buy 838,861 coins for 4 gold in Chapter 5.
Change Overworld music
In Chapter V, after you have found all seven chosen ones (Ragnar, Alena, Brey, Cristo, Taloon, Nara, and Mara), you can change the music on the overworld. Place Ragnar at the lead of the party if you want Chapter I music, place Alena, Brey, or Cristo for Chapter II music, Taloon for Chapter III, Nara or Mara for Chapter IV, and the Hero for all-new music. If you want the Hero's old music, set him/her at the head of the party with no one else in it.
Invisible Balloon (Japan-only)
If you sail to the coordinates 0,0 on the world map (this would be in the ocean northwest of Stancia) and press A on those coordinates, you'll board an invisible balloon. This can permit extreme sequence breaking. When you leave the overworld though it will return to its original location so take care.
View Poker Results
Go to the casino, start a Poker game, hold B and press Select + Start.