I'm searching for a serverless embedded noSQL document-store database for (mainly) Android and iOS.
To simplify, I need a document based SQLite :P
MongoDB is great, and has lots of drivers but it needs a server...
Maybe a stripped down version of it could be fine...
You should consider Parse.com. It's very easy to use. It's not serverless, but they provide the server and it's well worth it. It's free for small numbers of API requests.
Incidentally, it uses EC2 servers running Ruby and MongoDB and it's incredibly scalable. It takes almost no work and is on iOS and Android.