Can your parents claim you for taxes and you claim yourself?

In the US, when another taxpayer is entitled to claim you as a dependent on their income tax return, you cannot take an exemption for yourself even if the other taxpayer does not actually claim you as a dependent.

Then Exemptions for Dependents

Dependent not allowed a personal exemption. If you can claim an exemption for your dependent, the dependent cannot claim his or her own personal exemption on his or her own tax return. This is true even if you do not claim the dependent's exemption on your return or if the exemption will be reduced under the phaseout rule described under Phaseout of Exemptions, later.

Go to the IRS gov web site and use the search box for Publication 17 (2009), Your Federal Income Tax for Individuals go to chapter 3 Exemptions

You can click on the below related link