See also the answer that opens, "Looking for any information on person X..."
I see this as not so much a problem of on-topic or off-topic but scope, purpose and accompanying documentation. Regardless of the form, most of the questions I see in this category represent some modern notion of a traditional query.
Our challenge is to discover how Genealogy.SE becomes the place for content driven, valuable queries.
This is easier said than done.
In earlier times, many queries were published in journals or newsletters. Submitters often had to be a dues paying member of the publishing organization. Limitations as to length and/or frequency typically applied. Said another way, folks writing queries way back when had good reason to be concrete, to the point and on-topic. It took some thought and work; no doubt an editor helped many see the light.
And then we discovered the Internets.
While there are several modern guides, genealogist extraordinaire Kimberly Powell (about.com) has a nice article, "How To Write a Successful Genealogy Query."*
More than on-topic or off-topic, it seems we need "our guide" (and community protocols**) for this aspect of the Q&A.
*Including that Genealogy.SE would likely approach in her nos. 7, 9, 10 and 11 differently.
**How we address "queries" posted that are not a good fit (fall outside of "our guide")? As well, how to address non-response to suggestions about how to make the query a better fit.