Imagine you have two accounts at Gmail: One like myname@gmail.com, and the other like myname@mysociety.com (Using Gmail's hosted service). If you want to use two copies of Gmail Notifier to watch each account, you'll find that just duplicating the application is not enough. Instead, here's what you need to do:

1. Duplicate the Google Notifier application.
2. Select the duplicate, control-click on its icon, and choose Show Package Contents from the pop-up menu.
3. Navigate into Contents, and then open Info.plist in an editor.
4. There is a property in that file called CFBundleIdentifier, with the value com.google.GmailNotifier. Change the property's value to com.google.GmailNotifierMysociety instead.
5. Save your change and quit the editor.

With that change, the duplicated app will use a different preferences file, making the trick durable even after a restart -- unlike a simple duplication of the app. Howevever, the last problem is that the duplicated application's toolbar menu will be identical to that of the original, leading to confusion -- which menu leads to my main account?

To solve that, you'll need the Developer Toools installed. If you have them, inside the Gmail Notifier app (the copy you made), open Contents -> Resources -> English.lproj -> MainMenu.nib with InterfaceBuilder. Double-click on the BothMenu item and add an Item object at the end of the menu, and input myname@mysociety.com. Save your work, and you're done.

[robg adds: This hint replaces this older hint, which as the commenters noted, will not work across restarts.]