Blender
3D graphics software. Can kind of be used for almost anything graphics related. A bit hard to learn, but very powerful.
Inkscape
A vector art program. Great for logos or quickly generating graphics made out of geometric shapes.
Gimp
An alternative to photoshop. While it lacks the feature set of photoshop, I find it less crashy, and for some functions, it is actually faster than photoshop.
The two things I miss the most from photoshop are...
Predicting what would be behind an object when you delete it from a photo and smart selection that is much more responsive at separating foreground objects from the background.
Davinci Resolve
A free and powerful video editor. There is a paid version, but you get more than enough to get dangerous with the free version.
Browser Automation Studio
If you want to cheat at a web game or automate a repetitive process on a website, this is the go to. Makes it very easy to automate browser actions.
Touch Designer
A complicated one to explain. Designed for live and even interactive installations, this software combines node based programming, graphic manipulation and I/O control for things like LEDS or speakers or screens or projectors or you name it.
This is what you would use if you wanted to orchestrate something like what you see to the right.
You can do a lot with the free version.
ScreenToGif
Useful for quickly turning anything on your monitor into a gif.
Record a section of your screen to show a co-worker how to navigate a menu or turn a video you saw into a gif you can share.
Very easy to use, very useful.
VLC Media Player
A video player that can play almost any video and convert them to different formats, including ones well suited for YouTube. Useful for so many reasons.