Moving individual specific applications from Leopard to Mountain Lion
It depends, primarily on the way the application got installed initially


Apps which get installed by drag&amp;drop'ing the .app file into /Applications can just be copied to the new system. You will loose your preferences (unless you copied your ~/Library as well) but the application should work
Apps which need an installer may or may not work depending on whether the installer wrote stuff to other folders besides /Applications. Most installers probably do (there isn't a technical reason to use one otherwise)


And of course you need to keep in mind that PPC applications are no longer supported under  Mountain Lion.