I inheireted a house in 2001, and sold it in April of 2010. I did not buy another house. Do I have to pay taxes on the entire sales price ?

You have to determine the value of the property at the time you inherited it. That becomes your cost basis. You then pay taxes on the difference between the sales price and the cost basis, less any capital improvements made.

Your answer is one of about 6 I've received more than once... I can say it is running in first place, but until your answer it was in a three way tie. I'm thinking this is not the best way to figure out something as serious as dealing with the IRS.

Don't take my word for it. This is what the IRS says:
Inherited Property

Your basis in property you inherit from a decedent is generally one of the following.

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The FMV of the property at the date of the decedent's death.
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The FMV on the alternate valuation date if the personal representative for the estate elects to use alternate valuation.
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The value under the special-use valuation method for real property used in farming or a closely held business if elected for estate tax purposes.
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The decedent's adjusted basis in land to the extent of the value excluded from the decedent's taxable estate as a qualified conservation easement.

If a federal estate tax return does not have to be filed, your basis in the inherited property is its appraised value at the date of death for state inheritance or transmission taxes.

See IRS publication 17:
Publication 17 (2009), Your Federal Income Tax (http://www.irs.gov/publications/p17/ch13.html#en_US_publink1000172221)