The U.S. does not have an inheritance tax. Thus, any inheritance you receive as a beneficiary is tax-free to you (assuming relevant estate taxes have been paid). In limited instances the U.S. government may attach beneficiary inheritances where the estate were subject to U.S. estate tax and failed to pay prior to distribution to the heirs.
However, should you ever inherit a tax-deferred account such as an IRA, a 401(k) or pension account or an annuity, any distributions you take would be subject to income tax the same as if the decedent owner took a distribution. U.S. savings bonds are also taxable to you when redeemed. This is called income in respect of a decedent (IRD). If you inherit tax-deferred accounts seek competent tax counsel as you have significant choices to make regarding titling of the accounts and required distributions. Of course any investment income generated by the inherited funds (once you receive it) would be subject to normal taxation.
Except for items of IRD (see above) your cost basis in inherited property will generally be equal to the fair market value as of the date of the decedent's death (unless an estate tax return is filed and the executor chooses an alternate valuation date). Accordingly, if you sell the property you will only be taxed on post-death appreciation. The heirs are automatically presumed to have held any inherited property more then one year, thus entitling you to long-term capital gains rates if you sell. Thus, the maximum Federal tax rate on gains on the sale of inherited property is 15% (5% if the gain would otherwise be taxed in the 10% or 15% regular tax brackets).
Some states also tax beneficiary inheritances based on your residence status and your relationship to the deceased. If you indicate which state you are resident of I can confirm whether you have an inheritance tax issue.