My wife is British and doesn't have a SSN. How do I file as a married American?

We living in the UK together.  I'm applying for indefinite leave to remain in a few months.  However I'm trying to figure out how to file my American tax returns.  All the forms assume my wife has a SSN, but she doesn't..... I could probably figure out the rest if I could get around the fact all the forms assume my wife has a SSN....

Are you filing either married jointly or married separately but claiming your wife as a dependent?  If so, you need to apply for an ITIN using a W-7.  Here is a publication explaining how to apply for an ITIN: http://www.irs.gov/pub/irs-pdf/p1915.pdf.  You attach the W-7 to your 1040 and you leave the SSN field blank.

If you elect to file married jointly and treat your non-resident spouse as a resident, you will need to follow certain additional steps: http://www.irs.gov/Individuals/International-Taxpayers/U.S.-Citizens-and-Resident-Aliens-Abroad---Nonresident-Alien-Spouse.  Depending on your income situation, there can be significant benefits to filing jointly.

If you elect to file married separately but claim your spouse as a dependent, you can just file the W-7 along with your 1040. 

Either way, you will have to paper file, as you cannot electronically file a W-7.

(If you elect to file married separately but do *not* claim your spouse as a dependent, then you do not need to do anything extra.)