How much should I worry about black stools?

Check for bleeding. If your stools are black, tarry (sticky) and have a bad odor - this could be gastrointestinal bleeding and should be checked out promptly. As stated in a previous answer, some medications can cause black stools. It is simple to test the stool to determine if it contains blood.
Bleeding . You may be bleeding. Unless you are on peptobismol or iron supplements, your sstools should not be black. See a physician or go to er.