One to One such as any interaction between two modules or applications. You can connect your internal application with the one that has been developed outside your company as a 3rd-party application.
One to Many can be any notification or messaging system that you want to notify certain consumers or applications. For example it can be stock market, weather channel, event handler, message router, or anything like that.
Nowadays there are many projects in both academia and the industry. Just search in google and you can find plenty of them using JMS in their architecture. Another way to find real-life projects is to visit the website of famous application servers and you can see their customers.