I don't. I've corrupted SQLite DBs enough to not have warm and fuzzy feelings about it like I used to have.

I think it's only a good choice when you just need a database for your app that will barely be using it, and if you didn't use it you'd be writing to a file instead. And, that's basically what the SQLite docs say.

However, even then, I think it can be short-sighted. I've used webapps before that used SQLite and I thought to myself: if they'd only used MySQL or PostgreSQL and then provided access to it, I could have used it.

Be aware though, if you decide to use a scalable DB like PostgreSQL, it will require a port to be open for the DB, even if only locally. If you're trying to minimize how people can access your data, you don't want a port open/an extra port open, and you're not going to hit it very hard, SQLite's probably your best choice.