There is some projects that I usually do to get a feeling of the framework:
- Code snippets/tasks manager. Pure CRUD. If you want to get yourself dirty: add authentication.
- A blog (like SEJeff suggested). If you want to get yourself dirty: try to make it multilingual with SEO.
- Syllabication app. Helps me to find how business logic is best placed into app mindset.
I have to go, but if you need more examples just say! :)