Once you are at the page you want to add a web part to, add the following to the URL:
To change everyone’s view of a particular page, append ?PageView=Shared&ToolPaneView=2 to the URL.
To change your private view of a particular page, append ?PageView=Personal&ToolPaneView=2 to the URL (this will only work on pages that allow you to have a personal view – to see if you can edit a personal view of a page, go to the page and click on the top right context menu beside the "Welcome, <your name>" link to see if there’s a menu option called "Personalise this page").
More info on the URL switches can be found here – http://blogs.msdn.com/danielmcpherson/archive/2004/10/11/240863.aspx – they relate to 2003, but they all seem to work on 2007 as well.
I keep searching for this using google search and failing to find it, so now I’m going to flood it with keywords in the hope it comes up next time I need this string… admin flyout menu page view querystring tool pane shared personal 🙂