You should consider an application server when you have a need for:
Integration with existing systems and databases
Secondary reasons to use application servers derive from the primary reasons. A few secondary reasons are:
One way to look at application servers is that they are a formalization of a solution to a problem that has been around for a long time. That problem can characterized as a need to create an integrated presentation and processing environment for existing systems and databases. The presentation has pretty much been decided with browsers now being the dominant interface. This is why you usually see a Web server paired with or included in an application server. The integrated processing has been moving towards components for some time. Application servers provide containers for such components along with application program interfaces (APIs) to support the components. These APIs are to the existing systems and databases.