Some attempt to classify applications is made here:
http://en.wikipedia.org/wiki/Application_software
Here are a few examples:
Specializing the operating system's virtual office metaphor, productivity software often attempts to virtualize the office/studio of a writer, accountant, or artist. Here are a few examples:
word processors, spreadsheets, presentation software, diagram editors, drawing/painting
Here are a few examples:
Databases
Business workflow systems
Project management, security, human resources, ...
How would you classify computer games?
Image, video, sound editing
CAD/CAM
Flash, Dreamweaver, ...
debuggers, compilers, editors, bug reporting systems, version control systems,
social, scientific, military, games
Lots has been left out. What about social networking? Email? IM?