I fired up a new tool that's now included with Ubuntu Linux - Baobab. Baobab exists to provide me a graphical view of my filesystem, so that I can immediately tell what's taking up all of my space.
Turns out I'm taking up all of my space. I was shocked to discover a scant 7GiB left on my 120GiB hard drive. So where is all of that space going?
That space is being eaten up by my trash can. I have over 35GiB of downloads crammed into my trash can. There are a few other areas that could stand to be trimmed down, but nothing compares to the junk that I've downloaded and subsequently deleted over the past year (particularly multiple seasons of a particular TV show).