Here are a few of the software tools I rely upon often, and in my opinion make a valuable addition to your software library.
VNC (Virtual Network Computing) - A standard for many years for me. Having several computers and severs around the house I don't always want to operate each one from it on keyboard. The solution for me, is VNC (UltraVNC) to be specific. Running VNC as a service on the host machines that I want to remote control allows me to run the VNC viewer and connect to each. The servers running at my home have no keyboard, mouse or monitor, all operations are done remotely from a workstation using VNC. So if you have a need to do remote control, this is one fine open source alternative to commercial equivalents. Google search VNC and you will find many variations, so do a little research and find the one that appeals to you the most.
IRFanView - A popular image viewer that I have also used over the years. It will view almost any image format you can throw at it, and perform resizing/resampling of the images. Its free, quick and easy.
DVD Shrink - The handiest freeware I have found for backing up my DVD's. This software will backup your Video DVD's and remove the copy protection. It's not easy to find a good download link so try here
Audacity - Free Sound Editor and Recorder. Another superb project at Sourceforge. I use this tool whenever I want to edit any sound file. I've also used this program heavily while turning old LP's into MP3 recordings. If you have any audio editing needs this is the tool for you.
BadBlue - Is a File sharing web server that has easy setup and configuration. I've used it for several years and still do for my music files so I can access from anywhere. You might use for photos, or other files that you want to share with friends or family. Free version available along with several commercial versions.
Freesco - Free software for a very versatile and in-expensive do it yourself router. I used one of these for about 2 years and it is a rock solid open source project that can teach you a lot about networks and network configuration.
VLC - A cross platform media player and server. Support for many audio and video formats.