Is there a canonical "test SSN" that is used by convention, so is understood by all who see it that it is not a real SSN?
To expand on the Wikipedia-based answers:
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":
I'd consider that pretty definitive.
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":
But this is only a FAQ and it's never outright stated that "00" or "0000" will never be used.
In another FAQ they provide (http://www.socialsecurity.gov/employer/randomizationfaqs.html#a0=6) that "00" or "0000" will never be used.
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):