Deductions & credits

Paulsondw's answer refers to a special situation and is not a general rule. "NRA" can be entered if 1) US citizen or resident alien is married filing separately from nonresident alien spouse, 2) NRA spouse has no US reporting obligations (effectively connected income taxed by US) and 3) is not required to have a SSN or ITIN.

The default for a US citizen or resident alien married to a nonresident alien is to file separately. However, as the IRS notes, "you will generally pay more combined tax on separate returns than you would on a joint return" because there are a number of special rules and tax breaks you can't take when MFS.

US filers with nonresident spouses can elect to file jointly, typically to save on taxes. For MFJ, the worldwide income of both spouses is reported and taxed by the US.

Usually, the reason for filing separately is to exclude the NRA spouse's income (assuming none is US connected and taxable by US). MFS can be beneficial if the NRA spouse has a significant overseas income. In that situation, it is suggested that taxes be figured both separately and jointly, so the decision about which way to file can be based on the lower tax.

Entering "NRA" instead of a SSN or ITIN on a separately filed return precludes it from being filed electronically. The return must be processed manually by IRS.

Choosing to file jointly, however, requires that a SSN or ITIN be entered for the NRA spouse -- no exceptions. This requirement is part of the IRS' increasing vigilance about tax evasion.

For reference, here are excerpts from IRS Publication 17:

Nonresident alien spouse.
If your spouse is a nonresident alien, your spouse must have either an SSN or an ITIN if:
-- You file a joint return, or
-- Your spouse is filing a separate return.

Individual taxpayer identification number (ITIN).
The IRS will issue you an ITIN if you are a nonresident or resident alien and you don't have and aren’t eligible to get an SSN. This also applies to an alien spouse or dependent.
-- <a rel="nofollow" target="_blank" href="https://www.irs.gov/pub/irs-pdf/p17.pdf#page=12">https://www.irs.gov/pub/irs-pdf/p17.pdf#page=12</a> (column 1)

Nonresident alien or dual-status alien.
Generally, a married couple can’t file a joint return if either one is a nonresident alien at any time during the tax year. However, if one spouse was a nonresident alien or dual-status alien who was married to a U.S. citizen or resident alien at the end of the year, the spouses can choose to file a joint return.
-- <a rel="nofollow" target="_blank" href="https://www.irs.gov/pub/irs-pdf/p17.pdf#page=21">https://www.irs.gov/pub/irs-pdf/p17.pdf#page=21</a> (column 2)

Married Filing Separately
If you file a separate return, you generally report only your own income, credits, and deductions.

Select this filing status by checking the Married filing separately box on the Filing Status line at the top of Form 1040. Enter your spouse's full name and SSN or ITIN ... If your spouse doesn't have and isn't required to have an SSN or ITIN, enter "NRA" in the space for your spouse's SSN.
-- <a rel="nofollow" target="_blank" href="https://www.irs.gov/pub/irs-pdf/p17.pdf#page=21">https://www.irs.gov/pub/irs-pdf/p17.pdf#page=21</a>

For more complete information than provided by Publication 17, look at Publication 519, U.S. Tax Guide for Aliens
-- <a rel="nofollow" target="_blank" href="https://www.irs.gov/publications/p519">https://www.irs.gov/publications/p519</a>