There's a setting tucked away in the recesses of Firefox 3.5's configuration options that will keep the browser running after you close the last tab. Instead of closing, Firefox will simply display a single blank tab.
Here's how it works. Type "about:config" into the location bar (without the quotation marks), and then finding the setting labeled "browser.tabs.closeWindowWithLastTab" (again, without the quotes) and double click that setting to change the value to false. That's it. Now when you close all your browser tabs Firefox will stay open.