I never saw much of a reason for SQLite either until I started doing mobile development. However, it's nearly a must for doing any sort of intensive storage though with Android or iOS (unless use cases are simple enough for XML and JSON).
I just wish doing asynchronous queries with SQLite on Android was not so obtuse and resulted in a bunch of boilerplate or using third party libraries for a core part of the API.
On Android at least, I try to use loaderex[1] whenever possible, but it has some limitations. Best third party solution I've found so far. I was kind of fishing for someone to give some alternatives for Android and iOS, but seems like we're all kind of just in a rut :/
I just wish doing asynchronous queries with SQLite on Android was not so obtuse and resulted in a bunch of boilerplate or using third party libraries for a core part of the API.