How can I send HTTP requests from SQL Server 2012 to a non-.Net application?
You send a request, when you need something back. If you want to let someone to know something, but do not need anything back you notify with a notification. 

There is such a feature called SQL Server Service Broker. It allows communitaion over boundaries of different systems and guarantees consistency and timing of the messages.

Further reading:
 - SQL Server Service Broker  on MSDN
 - SQL Server Service Broker Explained