To answer your first question, TodoMVC (http://todomvc.com/) has a Meteor implementation: http://todomvcapp.meteor.com/

And for our Meteor book, we built a pretty standard forum/HN clone app called Microscope: https://github.com/DiscoverMeteor/Microscope

But I'm not sure what you mean by a Meteor app with a native client. Do you mean a native client that uses the DDP protocol (http://www.meteor.com/blog/2012/03/21/introducing-ddp) to communicate with a Meteor back-end? I haven't heard of that yet, but PiJS (http://pijs.io) uses DDP to do interesting things with the Raspberry Pi.