In my experience, you shouldn’t use a relational database when any one of these criteria are true:
- your data is structured as a hierarchy or a graph (network) of arbitrary depth,
- the typical access pattern emphasizes reading over writing, or
- there’s no requirement for ad-hoc queries.
Deep hierarchies and graphs do not translate well to relational tables. Even with the assistance of proprietary extensions like Oracle’s CONNECT BY, chasing down trees is a mighty pain using SQL.
Relational databases add a lot of overhead for simple read access. Transactional and referential integrity are powerful, but overkill for some applications. So for read-mostly applications, a file metaphor is good enough.
Finally, you simply don’t need a relational database with its full-blown query language if there are no unexpected queries anticipated. If there are no suits asking questions like “how many 5%-discounted blue widgets did we sell in on the east coast grouped by salesperson?”, and there never will be, then you, sir, can live free of DB.