Where does OS X store unsaved TextEdit documents?
For Lion: It is in ~/Library/Containers/com.apple.TextEdit/Data/Library/Autosave\ Information/, e.g. Unsaved TextEdit Document.rtf. 

Note that ~/Library is not visible by default in Finder in Lion, but you can access it by pasting the path in Finder (without the backslash in "Autosave Information"; the formatting above is for cd-ing in Terminal.app), or there is an option to enable the visibility (chflags nohidden ~/Library)

For Snow Leopard (credit goes to @binarybob, his comment is below) it is in ~/Library/Autosave Information also named Unsaved TextEdit Document.rtf