This morning I spent some more time messing around with Compiz. I followed this tutorial to add an alternative repository to my sources list that keeps a more up to date version of Compiz around. When I ran the install initially, it errored out and broke a couple of my packages, but after fully removing Compiz through Synaptic, I was able to get the install process to work with no issues. It added a number of plugins to Compiz, along with the Emerald Theme Manager.
After messing about with Emerald, grabbing some great new wallpaper from Open Source Wallpaper, and screwing about with the Gnome theme for a few minutes, I ended up with this desktop:
I think that this is a great improvement over the default desktop: