Should I file my 2008 U.S Income tax return as head of household, claiming my non- resident alien spouse as a dependent? The spouse and I both lived ouside the USA for the entire year and she has no U.S. income. I cannot treat her as a resident for tax purposes and file jointly or sparate as married because she has no social security number and is not eligible to get one. I cannot find any IRS publication that directly addresses this issue.

You selected wrong filing status on your 2008 tax return. Spouse is never a dependent on the tax return, and you are not Head of Household. Your U.S. Tax Return: Filing Status: Head of Household (http://taxipay.blogspot.com/2008/05/head-of-household.html)

If you are a U.S. citizen or resident and are married, then you can only file as married filing jointly (MFJ) or married filing separately (MFS). If you file joint return, then you will attach W7 (ITIN application) for your spouse with your tax return.
If you file MFS, attach W7 or write Non-Resident in place of her SSN.
It is normally better to file as MFJ. In that case, you must both report your worldwide income on the tax return, and your spouse is treated as resident for tax purpose.