Realm is a new mobile database that I should look at.
While there are many options for server-side databases, for mobile it’s pretty much SQLite. (Core Data uses SQLite.) A few people may be using LevelDB (which I’ve been meaning to look at). Perhaps some people are using Kyoto Cabinet.
I love SQLite. I’ve been using it since SQLite 2.something. I’ve just about made a career out of it.
But if you asked me if we mobile developers should have more options, I’d respond with an emphatic yes.