Recall from the Personal Exemptions lesson that each taxpayer is allowed a personal exemption (unless the taxpayer is claimed by someone else). Taxpayers who file a joint return may claim their spouse's personal exemption. On a Married Filing Separate return, taxpayers may claim their spouse's personal exemption only if the spouse had no gross income, was not filing their own return, and could not be claimed as a dependent by anyone else.
The same rules apply to a citizen or resident alien who is married to a resident alien.
Remember, a spouse can never be claimed as a dependent of the taxpayer.