Marital status for re-entering USA if you got married abroad without registering?

If I came to the US as a single student on an F1 visa, then during college vacation got married abroad (but did not register it in any country) is it okay to declare my marital status as single?

If your marriage was never registered (ie, there is no record of it), then you are legally not married. (See s.brody's answer on why this is important).

Secondly, if your union is not recognized - you may have get married again in the US in order if you intend to stay with your spouse beyond the remit of your F1 visa.

My spouse is a Green Card holder also living in the US. We just want to get married in Asia (we are both of Asian origin).

If you want to get married outside of the US, and use that union to enter and stay with your spouse, then the first condition is that your marriage should be registered and these documents (marriage certificate, notarized, etc.) are the first step in getting your permit to enter the US for the reason of staying with your spouse permanently.

Regarding your concern about re-entry to the US. As long as your F1 is current, and you are admitted for studies - then you can re-enter the US.

Once inside, it will be up to you and your spouse to decide what course of action to take, but keep in mind that you will need some documentation of your change in marital status in order to move things forward.

For more information on the requirements, you can refer to the instructions for filing I-130 (PDF), where you will see the following conditions:

1. You and your spouse have to be physically present at the ceremony.
2. The marriage has to be consummated.
3. As proof of your relationship, you have to present a marriage certificate.

Starting with a quote from Department of State website:

"Marriages performed overseas are considered valid in the country where they take place if they are entered into in accordance with local law".

Supposing you do want to get married legally in an Asian country, please do make sure you meet the requirements of marriage laws in that respective country.

Once the civil marriage takes place, and all papers are signed, the next step would be looking into getting it recognized in the United States. This is a case of a US Lawful Permanent Resident/ GC holder (that would be your SO), whose spouse (that would be you, on an F1 visa) is inside the USA through lawful admission. From this point on, my advice is to declare as married when required. I'm guessing you eventually want to become a GC holder, too, since you mention the intention of staying in the US. We're talking about Adjustment of Status, essentially. USCIS instructions are (quote):

"File Form I-130. After a visa number becomes available, apply to adjust status to permanent residency using Form I-485."

Make sure to maintain an original or certified copy of your foreign marriage document, along with a notarized translation. This will be required for tax purposes, or a change in your immigration status.

** Regarding tax filling, take a look here: IRS - U.S. Citizens and Resident Aliens Abroad - Nonresident Alien Spouse ** USCIS InstructionsBringing Spouses to Live in the United States as Permanent Residents