One of the important steps you need to do when setting up a new Drupal site is creating a cronjob that hits up your Drupal install. Or at least it used to be an important step in the past.  Poormanscron is a module that simulates a crontab by keeping track of the time and then running Drupal's cron task whenever a page on your site is loaded around the right time, and it has been added to core in Drupal 7.  Finding this out explained where all these mysterious cron calls in my log were coming from!

Even still, I wanted to go through the crontab setup process anyways, as I was learning the ins and outs of my new hosting company's control panel.  (And as mentioned, Poormanscron will only run when a page is accessed, so if your site doesn't get a lot of hits, your cron won't run as often as you like)