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.