There are two types of exemptions you can claim: personal exemptions, which you claim for yourself (and your spouse if you are married and file jointly), and dependent exemptions, which you claim for children or relatives you support.
To be a qualifying child, the child must live with you most of the year, be under age 19 (exceptions for full-time students and permanently disabled children apply) and not provide more than half of her own support. To be a qualifying relative, the person must live with you for the entire year, have more than half of his support provided by you, and not have income exceeding the annual limit, which is $3,800 for the tax year 2012.
The amount you can deduct for each exemption changes each year for inflation. For the 2012 tax year, each exemption decreased your taxable income by $3,800. The amount is expected to rise to $3,900 in 2013.
If your adjusted gross income exceeds the annual limits based on your filing status, the value of your exemption may be reduced. However, this reduction will not decrease the value of the exemption by more then 1/3 of its value.
The same person cannot be claimed as an exemption of two different tax returns. For example, if you claim your child as an exemption on your tax return, he cannot claim himself on his own taxes.