Believe it or not, Mac OS X lets you do this. The method used to do it isn't immediately obvious, however. Here's how it's done (this only works on .app packages and you need access to the Terminal): Select the application, Control-click it, and choose "Show Package Contents". Open the Contents folder, then the MacOS folder. You should see a UNIX executable in there with the same name as the .app package. Double-click that, and a new Terminal window will open, which will then start the application. Double-click it again, and you'll have two Terminal windows, two copies of the application open, and two icons for it in the Dock.
I just discovered this today, and I think it's kinda cool, although largely useless in most cases.
I just discovered this today, and I think it's kinda cool, although largely useless in most cases.