Most estates don't owe federal estate or gift tax, because you can give away or leave substantial amounts of property tax-free.
The federal estate and gift taxes are really one tax, called the unified gift and estate tax. For deaths in 2015, you can leave or give away up to $5.43 million, total, before you need to pay tax. Tax liability isn't assessed until death, unless you make $5.43 million in taxable gifts (very unusual) during your lifetime.
The personal estate tax exemption. The personal exemption allows a set dollar amount of property to pass tax free, no matter who inherits it. For deaths in 2014, the individual exemption was $5.34 million; in 2015, it is $5.43 million. The amount is indexed for inflation, so it will probably increase in future years. If your estate is worth less than the exemption amount--as are the estates of more than 99% of the population--it won't owe federal estate tax when you die. If you have made taxable gifts during your life, the amount of yourpersonal exemption will be reduced by the amount of those taxable gifts.
The marital deduction. All property left to a surviving spouse passes free of estate tax. (I.R.C. § 2056(a).) This deduction is available to validly married same-sex couples, but it wasn't until the U.S. Supreme Court's 2013 decision in United States v. Windsor. The marital deduction is not allowed for property left to noncitizen spouses, but the personal estate tax exemption can be used for property left to noncitizen spouses.
The charitable deduction. All property left to a tax-exempt charity is also free of estate tax. (I.R.C. § 2055(a).)
Special rules for married couples. A surviving spouse gets a big tax break. If the deceased spouse didn't use up his or her individual tax exemption, the survivor can use what's left. That gives the couple a total exemption of twice the individual exemption amount, which can be split between them in any way that provides the greatest tax benefit. For example, say a man dies and leaves $4 million to his widow; no estate tax is owed because property left to a spouse is tax-free. The widow then dies, leaving $7 million (her own $3 million plus the $4 million she inherited from her husband) to their children. Her estate won't owe any estate tax, even though the estate is over the exemption amount, because the estate can use some of the husband's unused exemption.
If you think your estate will be large enough to trigger federal estate tax, get advice from an experienced estate planning lawyer who can help you sort through your options. There are a few estate planning tools you can use to reduce estate tax liability. (For more information, see Reduce Estate Tax by Making Gifts and Tax-Saving AB Trusts.)
State estate taxes. Even if your estate isn't big enough to owe federal estate tax, the state may still take a bite. Many states collect either their own estate or inheritance taxes. (See Estate and Gift Tax FAQ.) If you live in one of those states, there's not much you can do to avoid paying those taxes, save moving to another state.
Learn about each state's rules.
For More Information
For a discussion of how you can plan to avoid estate and gift taxes, including giving gifts and creating an AB or bypass trust, see Plan Your Estate or Make Your Own Living Trust, both by Denis Clifford (Nolo). For information on paying estate taxes after a death, see The Executor's Guide: Settling a Loved One's Estate or Trust, by Mary Randolph (Nolo).