<p>What are the characteristics of a multitasking operating system?<br>
What makes it multitasking?<br>
Are there non-multitasking operating systems?</p>

A multi tasking operating systems is:
An operating system that gives you the perception of 2 or more tasks/jobs/processes running at the same time.  It does this by dividing system resources amongst these tasks/jobs/processes.  And switching between the tasks/jobs/processes while they are executing very fast over and over again.
Yes there are non multi tasking operating systems, example: commodore 64's OS (Commodore BASIC 2.0).  Probably some custom made software for some companies.  Perhaps like an ATM machine, or movie theater stub ticket system.