Is there a way to make the X button exit Spotify?

You can use Alt+f, x instead of Alt+F4 as a temporary solution to quickly close Spotify.

You can actually right click on the icon in the notification area and choose the open that says 'Hide from Taskbar when closed.' Then the [x] will actually close the program, not just minimize it.

Source: http://www.youtube.com/watch?v=X5reA9E7IjA

The current version of Spotify now implements this behavior. Simply closing the window will close the entire application and stop music from playing in the background.