I would recommend the following book:
The Expat’s Guide to US Taxes: 2001/2002 by Jane Bruno
It answered most of the questions I had on this question.
One thing that may be trouble in your case is that your wife has an SSN. If she obtained this SSN as a permanent resident and did not revoke her permanent residency, she may have some tax obligations to the US.
Otherwise your wife is a non-resident alien spouse and may or may not have to be taxes depending on the details.
If you have no children there’s two basic ways to file:
Married filing Jointly: You get the most deductions and so on, but you have to report ALL income for both of you. With the foreign income exemption this MAY be more advantageous. However, if you choose this method you have to continue using this method until you revoke it, and once revoked it is difficult to reinvoke.
Married filing Separately: You only have to report your own income, you can take your wife’s standard deduction as long as she has no US tax obligations. This MAY be more advantageous if your wife’s income is higher than yours, or your income is very low.
If you have a child or other dependent, you may qualify to file as head of household. There’s a lot of requirements here, but this is often the most advantageous ways of filing if you qualify. (Edit: See Publication 501 for details.)
Getting back to your wife’s SSN. Normally a non-resident alien spouse would not have an SSN, but would apply for an ITIN. This looks like an SSN but is a bit different. To get an ITIN one needs to fill out a form and take the required documents to AIT for notarization and send them to the IRS. You will then get back the number in about a month. You spouse will need either an SSN or ITIN for you to file your taxes. (Edit: AIT will copy and notarize the required documents. You do not need to send the originals if they have been notarized by AIT.)
I have just summarized some of the issues. The book above has most of the details and pointers to the IRS forms that will help. You can also call the IRS for advice. The Tokyo office is usually pretty helpful in dealing with overseas resident’s tax issues.