Specifically, I'd like to change the transparency of an already open Terminal.app window. I know I can change the settings and then open a new window, but I can't figure out how to make an already existing window transparent.
And no, I'm not interested in switching to another terminal program, thanks.
In Terminal.app, if you change the settings of any of the presets it will affect all open windows that use that setting. (I can confirm this for 10.4+)
So, if you click on the preset you used for the open Terminal window (most likely the one with Default in grey text below it) and go to the Window tab you can click on the Color picker under the Background header and change the Opacity.
As of Mac OS X Lion 10.7, Terminal allows separate opacity settings for active and inactive windows. So, you can customize a single settings profile to have the frontmost window be more transparent and background windows more opaque.
The question is about setting the opacity for Terminal, but if someone is interested in how to globally set transparency off, go to System Preferences -> Accessibility -> Display. Then make sure that "Reduce transparency" is selected. I found this here:
for Yosemite, but it works in El Capitan.