I have over $3000 of capital loss carryover from 2008. It was a loss from stock sales. I have no taxable income for 2009 (had income but less than total deductions). I understand that I am allowed to use -$3,000 of loss carryover to offset the income. When my total income is less than $2,000 and my taxable income is zero, do I still have to use - $3,000 of loss carryover? Can I carry the whole amount to 2010 instead?

No, you cannot carry over the full loss to 2010.

You must claim $3,000 of the loss in 2009, even if you do not need it and even if you do NOT file a tax return for 2009.