Types of Software

Software can be broken down into categories, based on what the software is used for. Here are some common categories, with examples:

Communication This would include any software that allows people to contact each other by voice or video, as well as text chat programs and email. Examples include Skype, Windows Messenger, Outlook Express, and Mozilla Thunderbird.
Design & Publishing This includes software which is used to edit photographs, create designs, author web sites, and other graphic design tasks. The most famous example is the Adobe Creative Suite (CS), which includes Photoshop, Illustrator, InDesign, and Dreamweaver. Other examples include Quark XPress, Composer, or Gimp.
Education This includes a variety of software intended for training and teaching. Much of it is specialized, but some apps are well-known. Among the examples are Mavis Beacon Teaches Typing, Mathematica, and even Google Earth.
Games This is exactly what it seems--gaming. Examples include World of Warcraft, Solitaire, Civilization, The Sims, Halo, and of course many others.
Internet While browsers often have their own category, they could be fit here as well. Also included are apps for Blogging, P2P/File-sharing, FTP, and Social Networking. Examples include Ecto (blogging clientA "client" program is one that connects to a larger application on a network, usually online), BitTorrent, FileZilla, and various Facebook and Twitter clients.
Music & Audio This would include Music Players, Audio Editors, and Music-related apps such as cataloging and other tools. Examples include iTunes, Windows Media Player, and Audacity.
Office This would include what are known as "Office Suites," program groups which include Word Processing, Spreadsheet, Presentation, and Database software. Examples include Microsoft Office, Open Office, Star Office, or iWork.
Operating Systems This would include Windows, Mac OS X, and Linux, as well as Unix and older operating systems like MS-DOS and OS/2.
Productivity This category describes software which helps you in daily work and tasks you must do. It includes Calendar, Finance, Note-taking, Organization, and specialized Text-editing software. Examples include Quicken, or Foxit PDF Reader.
Utilities These are usually programs which allow you to check, change, protect, or repair your hardware or operating system software. These include disk utility programs, anti-virus software, data backup, and data recovery software. Examples include Norton Utilities or WinZip.
Video This would include Video Players, Video Editing (and "encoding" software for translating between file types), and other video-related software. Some of these overlap with Music apps, as they plays both music and video files. Examples include VLC, Movie Maker, Handbrake, and Final Cut.

There are other categories one could make, and different sources sort software into different varieties of categories; few sources have the exact same system. The above, however, gives a fairly representative sample, however.