Switching Page Layouts and your web parts went missing?

If you switch the page layout of a page, and the new page layout has different web part zones, you might lose the web parts you meticulously setup.  But they're not gone.  You can go to the page and go to the web part view by adding ?Contents=1 to the the url and you'll see the web parts:

If you just select them and press close, they'll show up in your Closed Web Parts section:

And then you can just add them back to the new web part zones!