It heavily depends on the application.
If you have installed the application from the Software Center, then I guess you will not have a problem re-downloading and re-installing it through there, you just want to keep your settings. If this really the case, then you have to look under your home folder.
The first place to look is under
~/.config/Application_Name and under
Usually, if you backup these folders you will successfully save the configurations of your applications. But, unless you are more specific about your application, I cannot search and see myself.