Heart Gold and Soul Silver: Mom's Savings
At the beginning of the game, your Mom will offer to save your money. If you choose yes, you will send half of your winnings to your Mom after each battle. This can amount to a lot of money by the time you beat the Elite 4 for the the first time. You can access your savings at any time throughout the game and even stop your Mom from saving your money by calling her.
If you do choose to have a savings account with your Mom, she will occasionally buy items for you with your money. This might sound like a bad thing, but she does buy worthwhile items sometimes. For example, your Mom will buy a Moon Stone, a Choice Scarf, a Muscle Band, a Focus Sash, and rare berries from time to time. When your Mom buys an item for you, she will call and tell you to go to a PokeMart. When you go to a PokeMart there will be a man in a red uniform and hat by the counter. Talk to this man and he will give you the item your Mom bought. Make sure to talk to the man until he tells you he has nothing left to give so that way you get everything your Mom has bought.