Kids Saving
Kids can learn how to start saving at an early age. Savings really compound and multiply the more time you have for an account to grow.
Younger kids can learn the power of saving by taking say part of their allowance and putting it into a savings account. Just seeing 5$ become $10 and adding to that until it is $100 and then $1000 can be very satisfying and that positive experience can help kids save even more.
As kids get older they can contribute themselves with money the earn on their own. It is always a good idea to set aside a small amount from any income into savings and it is ok to buy something with some of the money as a reward to repeat the action of working and getting more money, a great positive cycle.
Ways kids are saving
Kids can save actual money they earn, money they receive as allowance or gifts from relatives or birthdays.
Kids can also save household money by simply shutting off unused lights, powering off electronics when through, not leaving Nintendo and other charges in the walls when not charging as these wall warts can continue to drain electricity while just being plugged into the wall even if they are not currently charging a device.
Kids can help with certain chores instead of paying someone else to do them and can learn in the process. Kids can also save money by thinking about a potential purchase before just getting something, perhaps researching it a bit, asking friends for their opinion. More than one toy or game (or even game console, wii anyone?) has gone unused for long periods of time when the novelty of getting the item quickly wanes.
On the other hand kids are very happy when occupied with things they enjoy, and those items are priceless. It may be better to spring for that trampoline (with a safety net and pads of course) rather than buy a third video game console. Kids will have exercise, a variety, something to do with friends and increase their own mobility and dexterity. Perhaps matching funds can be used to encourage kids to save for something they really want and perhaps they will then have had the time to think about whether it is really something they will use once they get it.