Just off my basic understanding of how the database works, I don't believe a production web app would be a very appropriate use-case, since considering it's an embeddable database you'll be bound by the slow filesystem. Mysql/postgres or mongodb would be better options. This is more for self-contained applications such as cron jobs or utilities.
Since the underlying storage system is based on a modified version of Tokyo Cabinet [0], I don't see why it wouldn't be appropriate for small apps where a discrete DB would be overkill.
Again, I must offer a disclaimer that I only read a fraction of the total source code, but I would assume it would involve similar use-cases to sqlite [1]. For example, IIRC, the Firefox web browser uses (used?) sqlite for storage. However, reading over the list I just referenced, I must correct myself and say that for most websites, you would probably be ok in using it; however, this seems to be an embeddable replacement for mongodb, which is typically used for high-traffic environments anyway. I'm coming more from a background of high-traffic sites with large datasets, so I typically rely upon more tailored solutions, but I should be careful not to see everything through my own narrow perspective!