Numbers that have been misused in any way, such as the well known 078-05-1120.
Consider using one of these (the obviously invalid 000-00-0000 would be a good one IMO).
(Answer has been updated to provide source information beyond Wikipedia and remove information that is no longer accurate after the SSA made its randomization change in mid 2011.)
The Social Security Administration (SSA) explicitly states in this document that the having "000" in the first group of numbers "will NEVER be a valid SSN":
However, that the 2nd or 3rd groups of numbers won't be "00" or "0000" can be inferred from a FAQ that the SSA publishes which indicates that allocation of those groups starts at "01" or "0001":
I can't find a reference to the 'advertisement' reserved SSNs on the SSA site, but it appears that no numbers starting with a 3 digit number higher than 772 (according to the document referenced above) have been assigned yet, but there's nothing I could find that states those numbers are reserved. Wikipedia's reference is a book that I don't have access to. The Wikipedia information on the advertisement reserved numbers is mentioned across the web, but many are clearly copied from Wikipedia. I think it would be nice to have a citation from the SSA, though I suspect that now that Wikipedia has made the idea popular that these number would now have to be reserved for advertisements even if they weren't initially.
The SSA has a page with a couple of stories about SSN's they've had to retire because they were used in advertisements/samples (maybe the SSA should post a link to whatever their current policy on this might be):
The SSA is instituting a new policy the where all previously unused sequences are will be available for use.
Goes into affect June 25, 2011.
Taken from the new FAQ:
What changes will result from randomization?
The SSA will eliminate the geographical significance of the first three digits of the SSN, currently referred to as the area number, by no longer allocating the area numbers for assignment to individuals in specific states. The significance of the highest group number (the fourth and fifth digits of the SSN) for validation purposes will be eliminated. Randomization will also introduce previously unassigned area numbers for assignment excluding area numbers 000, 666 and 900-999.
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Will SSN randomization assign group number (the fourth and fifth digits of the SSN) 00 or serial number (the last four digits of the SSN) 0000?
SSN randomization will not assign group number 00 or serial number 0000. SSNs containing group number 00 or serial number 0000 will continue to be invalid.
If your testing requires pulling quasi-real credit reports from the bureaus, the inactive SSNs of other answers won't work and you'll need designated test numbers.
I found this site Which appears to contain test social security numbers with associated test names and credit card numbers.
Transunion has a test environment you can link and send data to, including associated dummy credit reports. Sending a SSN to them with certain numbers in certain positions will automatically route the inquiry to their test environment Other credit bureaus will have similar systems in place.