Runs even after logoff

Without the use of services, is it possible to create an app that, once run, continues running after the user has logged off? You know .. doing mundane things such as .. oh I don't know, counting seconds, playing checkers with itself. Something. I did some google research, but all I can come up with is "make it a service like this" or something to that extent. What if it's under an OS that doesn't support services like windows 95 or 98? (Those don't support services, right? Or am I just mistaken?)