There's another question about production apps, so I'll focus on open source examples here.
The main example app we have, which covers a relatively large range of features, is GitHunt: https://github.com/apollostack/GitHunt
This app includes examples of queries and mutations, and how those might work with routing, UI components, etc. There are directions for how to run the app in the repository.
You can also look at the home page of our docs for more community-contributed code samples: http://docs.apollostack.com/#Example-apps