Want to learn a new technology\framework\language\etc ? - write a chat app! So did I. This app allows anyone to chat (and even to send images!) in the global chat room on his WP8, iOS or Android smartphone.
Server side is built using DDD approach, data is stored in SQL using Entity Framework Code First, and transmitted using low level sockets (I created my own WCF :)
Client side is built using amazing Xamarin.Forms with MVVM approach.
Video:
Egor Bogatov