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.
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.