AdobeReader_enu-7.0.9-1.i386.rpm installs two Adobe Reader menu entries in the Applications menu. It puts one in /usr/share/applications and one in /usr/share/applnk/applications. Seeing as all the other menu items are in /usr/share/applications, I removed the one in /usr/share/applnk/applications.
Now I only have a single menu item.