Yes, in certain circumstances.
The income taxes must be more than 3 years old, measured from the "due date" of the tax return. Example: 2009 income taxes were due April 15, 2010. So you would have to wait until April 16, 2013 for the taxes to be old enough to be discharged in bankruptcy.
But if you requested an extension of the filing date to October 15 of 2010, your due date is now Oct. 15, 2010, and a bankruptcy would have to be filed more than 3 years later, or Oct. 16, 2013 or later, for the taxes to be discharged.
There are other requirements for income taxes to be cancelled in bankruptcy. The income tax return at issue also has to be filed more than 2 years before the filing of the bankruptcy, and the taxes at issue cannot have been assessed within 240 days of the filing of the bankruptcy.
Also, for the taxes to be discharged in bankruptcy, the income tax return cannot be false or fraudulent. And the taxpayer cannot have willfully attempted to evade or defeat the tax.
Also, even though you may be able to discharge income taxes, if the IRS has filed a notice of federal tax lien against you, the lien does not automatically go away. It remains effective against any property that you owned when you filed the bankruptcy. But at least if the taxes are discharged, the IRS can no longer levy you, or seize your money or property from a bank account or your wages, for example.
I don't recommend that you try to handle a bankruptcy case where you are trying to discharge income taxes yourself. It is even more complicated than I can explain here, as certain events can "toll" or stop the time periods from running and even extend the time periods.
So if you owe income taxes and are thinking about using bankruptcy to either pay or discharge them, hire an experienced bankruptcy attorney that is very familiar with the dischargeability of income taxes in bankruptcy.