I am a US citizen with Canadian permanent resident status. I am living in Canada with my spouse who is a Canadian citizen. They have never lived, worked, or gone to school in the states, they have only ever visited. They do not have a SSN or ITIN and do not want to get one. I am attempting to file my 2011 taxes, I got an extension to October 15th, and I am having trouble when I go to e-file my return without anything in the SSN box for my spouse. Is it possible to e-file without an SSN or ITIN? If I am not able to e-file, what do I put in the SSN box when I go to mail in my returns? This is for both federal and a single state return.

You cannot efile without an SSN/ITIN for your spouse.
When you paper file your return, write "NRA" (non-resident alien) in the field.

The procedure that TaxForaliens recommends works for the federal return and should work for the state return, but each state is different.