Services hang at boot after applying security updates to RHEL 6.0, 6.1, or 6.2 (or updating rsyslog only)

Issue

• I ran yum update --security on a Red Hat Enterprise Linux 6.0 (or 6.1 or 6.2) system and after rebooting, the system hangs.
• After updating some (not all) packages on a Red Hat Enterprise Linux 6 server and rebooting, the system hangs in the middle of the boot process when starting nfs statd. Disabling nfs leads to autofs hanging the boot process; disabling autofs leads to mcelog hanging. Disabling that leads to postfix and qpidd also hanging. If all these services are skipped, the system will get to a login prompt but will hang after the password is entered.
• I updated only the rsyslog package and now the system won't boot -- various services hang at boot-time.