Web Browsing -
Application: Mozilla Firefox
Many of us have at least heard of this one. It is easily the most popular piece of open source software out there. It job is to replace Internet Explorer if you are on Windows or Safari if you are on OSX. Firefox is a wonderful upgrade because in addition to running faster than most other browsers it is also the most secure. Meaning less viruses and Mal-ware for all you Windows users out there.
Office Suit -
To pick up the latest copy of Microsoft office odds are you are looking at spending a couple hundred dollars. OpenOffice is a full featured office suit, it contains a Word Processor, Spreadsheet, Power Point, Drawing, and much more. It opens and saves files in all the standard .doc, .ppt, .xls, formats so it is full compatible with all MS office files.
Many of us are aware that the quickest way to non-functioning Windows system is to catch a virus or two. Avast is one of the best anti-virus programs out there. It provides real time protection with minimal resource usage. It is free for home use so long as you are willing to register each year for a new key (which is a short and easy process)
Application: Spy Bot Search & Destroy
The Windows system is riddled with holes and exploits just waiting to make your life in front of the computer that much harder. In addition to having an awesome name Spy Bot S&D is the best program out there for hunting down malware that has found it's way into your unsuspecting system. The only slight draw back to this one is that it is NOT real time protection, meaning you need to remember to run the update for it and scan your system each week.
Compressing files is useful when you are trying to to send a large amount of files to someone or simply for storing files that is not often used often. 7-zip contains a custom archiving format, .7z, that is much more efficient than the standard .zip. In addition to having this custom format it also can compress into the more universally standard .zip in a more timely manner than the built in Windows compression software or commercial software such as WinZip
Instant Messaging -
Pidgin is a full featured instant messaging client similar to Trillian. It can connect to a wide range of networks, from AIM to Facebook, to Yahoo and MSN. It contains a logging feature that can be easily toggled on and off, along with a pile of other useful and fun plugins.
Photo Editing -
Gimp is a tool for manipulating images on the computer. In contains essentially all of the features the commercial soft Adobe Photoshop does. If you are already familiar with the Photoshop GUI there is also a plugin for Gimp called “Gimpshop” that makes Gimps GUI mirror that of Photoshop's.
I just highlighted a few of the more popular applications here but there are literally hundreds of free/open source applications out there for almost every task imaginable. From GNUCash (money management) to Kompozer (web-development) you can find just about anything you need. This website: http://osalt.com can help you easily locate what you are looking for.