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I don't think there's an established NoSQL backend for native mobile apps, but Couchbase Mobile is a great NoSQL database with implementations for both iOS and Android.
iOS: http://www.couchbase.com/products-and-services/mobile-couchbase
Android: https://github.com/couchbase/couchbase-lite-android
I wouldn't be surprised if there's a Tokyo Cabinet port for mobile OSs; but seriously, what would NoSQL bring over the SQLite library already included in every platform?
in short, you can just use SQLite as a 'small NoSQL' if you want. it's quite fast too.