Married couples can double this amount by gift-splitting; a gift of $26,000 from one spouse is treated as if it came half from each.
Gifts do more than help out children who need the money. They also reduce your estate so your estate will pay less estate tax upon your death. Apart from annual gift giving, you can currently transfer (during your lifetime or through your estate) a total of $5,000,000 with no estate or gift tax liability. On amounts above this threshold, you or your estate will be faced with taxes at the current top rate of $35%. So a consistent program of annual gift giving might create substantial tax savings.
Note that gifts to individuals do not entitle you to an income tax deduction. A gift isn't a charitable contribution. Conversely, a gift doesn't constitute taxable income to the recipient. Gifts of income-producing property may, however, reduce your taxable income. Once you've given the property away, the recipient, not you, receives the income it produces and pays any income tax due on it.
One advantage to annual gift giving is that it is relatively simple to do, especially if you're giving away cash. Another advantage is flexibility. You're not locked into anything; you can see how much you can afford to give away each year. You can give away anything - cash, stock, art, real estate. Valuation is the fair market value on the date of the gift. Subsequent appreciation, if any, belongs to the donee's estate, not yours.
Before you give away assets, be sure you will not need them yourself to provide income in later years. Consider the impact inflation will have on your resources.
Proper planning is essential in this area; get professional assistance before you do any gift giving.