It is highly recommended that you file as 'Married filing separately'.
You need not disclose your spouses' income from Canada, and your spouse 'technically' does not need any ITN to list on the tax forms. You only need put his/her name.
If you have filed as single previously and have gotten a refund based on EIC, you could be accused of tax fraud which would have implications beyond just what you might have to repay to the IRS.
I would strongly suggest you file as married, because you ARE MARRIED, whether your spouse lives in the US or Canada or Japan is not the point. There is a reason why they make these classes, because each has it's own set of rules and guidelines.
Tax law states that you must file married joint/ married filing separate or head of household if you are married. To qualify for the latter, you would need to meet some criteria. The law is pretty clear about this, even if it is only tax law it's still law and should be followed lest your risks increase exponentially.
To answer the other part of the question, you only need to file your standard 1040 along with the 8965 (if you live in Canada - it's for the Obamacare waiver bit) and if you have any retirement accounts in Canada they are also subject to IRS taxes. I can't remember the amount, but I believe it is 25K or more. The specific forms required can be found on the IRS.gov website.
If anyone would like to read about the facts I have noted, then look up publication 17 @irs.gov. This will give you classes/definitions and help you to determine even further which class you should be filing under.
If any of you who have been filing as single with low income have managed to get EIC; even though you were in fact married; I suspect you might want to consider filing an amended return.
Fun FACTA (yes, I intentionally spelled it that way), the IRS and CRA share your information
If your spouse filed married the IRS already knows ...