One of the new features of Mac OS X Lion is the Mission Control. This desktop management system can control where on the multiple desktop your window will appear. If you have a fresh install of Lion, you'll notice that by default, Finder will always follow you on all the Mission Control desktop you have. To change this behavior, or any other apps behavior, you can two-finger click the app on the dock, (or right click if you're using a mouse) and go to Options and pick where you'd like to assign your window.
|To make a window to appear on all Desktop in Mission Control, two-finger click (or right click on the mouse) and go to Options > All Desktop|