If you are filing a joint return, the alien spouse must have a SSN/ITIN. If you are filing as married filing separately, then the alien spouse does not need a SSN/ITIN, and you can put "NRA" in the space for the spouse's SSN.
The difference is that, if filing as separate, you only report (and pay taxes on) the US citizen spouse's income, and get only one exemption. If filing jointly, you must report and pay taxes on both spouses' incomes, but you get 2 exemptions.
