This amazingly useful web site makes upgrading Drupal much easier.   However, while following the steps, we encountered an error when trying to dry run the update:

patch -p1 --dry-run < PATCHFILE

	patch: unrecognized option `--dry-run'

Patch utility on our FreeBSD installation did not have --dry-run option available.  Instead, there is a --check option:

patch -p1 --check < PATCHFILE

The rest of instructions applied just fine and we upgraded from 6.16 to 6.19 in no time.  Just remember to back up your databases and files, just in case.