That's a really broad question, but asp.net mvc is suitable for really any type of application. It has great features for binding data and offers you much customization. If you want to really learn the framework I would consider building a custom model binder, custom attributes and work on creating custom routes.

Also look up unit testing and test driven development. One of the nice things about asp.net mvc is that it was built with testing in mind and they make it really easy to test your applications.

The mvc music store is a great resource to get started
http://mvcmusicstore.codeplex.com/

The tutorials on this site are great
http://www.asp.net/mvc/tutorials

This book is a really good book that will cover everything from basics, to all the foundation you need
http://www.amazon.com/Pro-ASP-NET-MVC-3-Framework/dp/1430234040

lastly, if you want to see (and learn) the future of mvc and webapps. Take a look a this video on single page applications, this is really cutting edge stuff
http://channel9.msdn.com/Events/TechDays/Techdays-2012-the-Netherlands/2159