I worked at a company which sells document archiving to businesses, and they do not use a database. All data is stored on disk in files. They use indexing of archived data, similar to how google indexes everything (they don't use google). They also use indexed files to keep track of some data, but most of it is about users+permissions, not much to do with data.
I don't feel I can give further details, but the company is making money, nothing you'd read about, but it's doing OK. Solution scales up so that insurance and financial companies are their clients. Terabytes of data - no big deal, it's quite amazing to see how much faster it runs on customer's computers with terabytes of data, than in house with test-databases on developer's PC's with only 100 MB of test data. And it doesn't even require an admin (besides someone to make sure there's enough space on disk).
I think it really depends on your app. Databases aren't always the right answer, but no one has been fired for using databases. (maybe that's why people flock to them - that, plus if everyone's doing it, and you are worried about your resume ... well ... you better do it too)