Under current tax law, every American starts life with a $675,000 lifetime exemption against gift and estate taxes. That means you can receive that amount personally before taxes kick in. But in circumstances where your spouse's entire estate passes to you, you could end up being taxed twice: First when you receive a bequest that totals out your spouse, and then again when that estate passes to your children.
By using what's called a qualified disclaimer, surviving spouses can make it so that estates never pass to them, and instead go on to their children (or whoever is specified in the original language). Or, through creating a marital trust, a surviving spouse can equalize the couple's two estates without combining them. Used together, these strategies are helpful because estate tax is progressive: One big estate owes more taxes than several smaller ones of equivalent value.
Grown children can use disclaimers in the event that their own estates are substantial -- playing disclaimers off the generation-skipping tax exemption -- so that the money never touches them. Instead, it would go on to the surviving grandchildren.
The IRS even allowed one woman, who owned half her husband's stock and inherited the other half after his death, to disclaim her inheritance (it passed to their son) and then sell her own shares. This made her son the sole stockholder and owner of the business.
Likewise, if you've inherited a charitable remainder trust -- one that provides for your lifetime, then donates the rest -- you can get a huge tax credit for the estate by disclaiming that trust and passing everything on to charity. In cases where you're already comfortable and don't want the tax burdens of the estate to complicate things, this is a great way to clear up any lingering tax issues you find yourself dealing with.