Is there a keyboard shortcut or some kind of setting to make the current window transparent?
I go back and forth between windows a lot. If I could just make the window I'm looking at transparent, it would be nicer.
AutoHotKey can do it! No fancy glass effects, but the window goes transparent. That's on Windows Key and Space.
There is no built-in shortcut that comes to mind, only one that makes all windows transparent:
However this isn't very useful for your situation.
Take a look at TweakWindow. It worked for me on Vista, not sure about 7. It has a useful "Make it Ghost" feature which not only makes the current window transparent, but also allows you to click through it: