What scenarios benefit from Mac OS X allowing apps to run when no document windows remain? As a rule of thumb programs on Mac OS X stay running when you close all their document windows.

This is the behavior I noticed in MacVim, VmWare Fusion, Chrome and host of other applications.

I personally find this of no use and frankly quite annoying, although having had some number of experiences confirming that my opinion is not always the prevailing in a given target group, I assume that there could be a reason for this decision.

What are scenarios where this function could be useful?
When you are using Windows and you open an application like MS Word or Adobe Photoshop, it will open up the application window with some sort of empty background. When you do this on a Mac however, there is no background, there is simply the menu options in the very top bar. So say you had a file open in Photoshop in Windows and you closed that file, you would see the same blank application window that you saw when you started up Photoshop. On a Mac, you will see the menu in the top bar, but again, since there is no background you simply see the desktop. So really, there is no difference in the way that Windows and Mac OS X handle the applications, other than one had a visible window and the other doesn't.

The benefit of doing it the OS X way: If you DO plan on keeping the application open, it keeps you from having to minimize the app like you would in windows. All you have to do it click on something else in the background and it will make the applciation lose focus. To close it, simply right click on the application icon in the dock and choose 'Quit'.