To be clear: applications create various files or store databases, which are independent of applications proper. For example, if you backup your data and settings in view of a new install by erasing the disk, you must not save applications, most of them are anyway installed by default together with the system, e.g. Mail, Safari, Address Book and the rest of the Apple basic set.
Therefore, a good backup saves your files, database and settings, not applications, unless they are 3rd party apps, which you wish to keep. Note that some apps require to run their installer, you cannot save them by moving from one location to another. For these apps, only cloning the partition solves the issue, but in some instances this is not necessary or even recommended.
As a thumb rule, all your files, databases and settings are within your login name, not elsewhere. Desktop files are also there in the folder labelled Desktop, settings in various locations of the Library (at the user level, not the /Library or /System/Library).