When should one use asynchronous controller in asp.net mvc 2?

Only use async if the operation is IO bound. A good example would be aggregating RSS feeds from multiple servers and then displaying them in a webpage.

See:

• http://msdn.microsoft.com/en-us/magazine/ee336138.aspx
• http://blog.stevensanderson.com/2008/04/05/improve-scalability-in-aspnet-mvc-using-asynchronous-requests/

for a good overview of asynchronous controllers.

And for more in-depth but non-MVC specific info: http://blogs.msdn.com/tmarq/archive/2010/04/14/performing-asynchronous-work-or-tasks-in-asp-net-applications.aspx