I think you should assess databases on a case-by-case basis, rather than adopt a single approach.
The main two criteria would be the nature of the data in the DB & how it was used: if it is a relatively simple thing that can be accurately represented in a in a single tabular structure then sure turn it into a CSV. If the DB was only ever used by end users to generate PDF reports, maybe you could just export all those reports.
Of course many relational databases aren't like that & in those cases I think flat formats like CSV or hierarchical ones like XML are a bad fit. But that doesn't necessarily mean you are stuck with the original. Why not migrate the DB into SQLITE? It is open source, cross platform, public domain and a single file format. If you hand write the schema during the migration you can add comments so the thing becomes (relatively) self-describing. RDF using something like http://www.w3.org/TR/r2rml/
might work too & would allow you to integrate that particular DB with other ones in your collection.