This week's book giveaway is in the OCMJEA forum. We're giving away four copies of OCM Java EE 6 Enterprise Architect Exam Guide and have Paul Allen & Joseph Bambara on-line! See this thread for details.
When the application is a server based application.
Even without multiple users, you may want to have background processes using the database asynchronously. Turn the question on its head: why do you think it is a good thing to restrict an application to one connection?