Ensure to write "return service requested, do not forward. If they have filed a change of address form with the USPS, you will get the letter back with a new address.
Call 411 or use an online telephone directory
Ok, I know this sounds silly, but often times if you call the city that you think your ex lives or works, you may be able to get a phone number and/or an address! If you know his/her phone number, try to get the address from a reverse telephone number directory.
Contact relatives or friends
If it is a divorce or child custody matter, perhaps you tell them that the children have an urgent matter and you need to contact the other parent? (It's not really a lie right? I mean if a parent is missing, that is certainly urgent!) Call, write or email them and ask if they contact information or, in the alternative, if they will contact them on your behalf.
Try past employers
Contact them to see if they have any info regarding the person's whereabouts or a name / address of a new employer. It's worth a try!
Search property records
Look to the tax assessor's office or county registrar/recorder's office to find contact information.
Consider using a paid internet site that searches for people
The more info you have like name, date of birth or social security number -- the more likely the results are accurate.Also try aliases.
If you think they might be in jail
Contact the State Department of Corrections, County Jails search the Federal Bureau of Prison's Inmate Locator Database. Make sure you have the name and date of birth.
Contact a private investigator or be your own detective.
Even if you don't know where someone lives, you may know where they frequent or know their habits. Do they go to a certain bar? Gym? Coffee shop? Remember, you can't serve him/her but you can have a friend, family member or registered server help you track someone down.