Generally, inherited property (including cash, stocks, and real estate) is not taxable or reportable on a personal1040 federal return.
However, any income earned from an inheritance such as interest, dividends, rent or capital gains will be taxable.
An inheritance will be taxable if you inherit an IRA, 401(k) or other retirement account and receive a distribution. That would be considered "income in respect of a decedent" which is earned by a deceased person prior to death. Because it was paid after death the income is taxable to the recipient in the year paid.
Only a handful of states (Iowa, Kentucky, Maryland, Nebraska, New Jersey, Pennsylvania and Tennessee) have some kind of inheritance tax. Refer to your state's Department of Revenue to see what the requirements are for filing inheritance tax.
Note: Ohio Estate Tax has ended. The Ohio Estate Tax was repealed effective January 1, 2013. There will be no estate tax on estates of individuals with a date of death on or after January 1, 2013. This legislative change occurred with the passage of the 2012-2013 Budget Bill, House Bill 153.