You’re not obligated to use categories. The listing of categories is a function of the theme, you can edit your theme and remove that. Depending on the structure of your theme these may be in a number of places. You can search for instances of get_the_category and comment them out. Look for a file called loop.php first, failing that, your single.php and index.php files.
*edit:
I should mention, it may be the case that your particular theme doesn’t allow you to remove the category listing as easily as I’ve outlined, if you’re using a framework based theme where these functions are removed from the normal template structure for instance. In this case you should seek assistance with the support of whomever developed your theme, or choose another.