PG writes in the Viaweb FAQ that they (and Yahoo) did not use any database, just files. It makes sense... Is there something fundamentally different about your app, so that a DB is obviously a better choice?
I think something is different about databases since then. You can, for free, install a database in part of an afternoon that has excellent library/framework support and tools. That makes a big difference. If you're going to use Ruby on Rails, for example, you will have to justify why you don't want to use database software.
Basically, databases have been well-commoditized, like Unix, HTTP servers, and hosting. If your needs fit their common usage scenarios, you should just go ahead and use them.
