Kernel This should be the first file backed up. If it gets deleted you can restore it back. This file is often named /kernel, /unix, or /vmunix.
Password File Having a backup of the password file is a good idea, in case the system password file gets compromised. This is the file referred to as /etc/passwd.
Group File Back this up for similar reasons as you do a password file. This file is /etc/group.
Host Table Make an extra copy of the host table, in case the file is corrupted or entries are removed and then needed in the future. This file is named /etc/hosts.
Filesystem Table This is for recovery of the filesystem configurations. This file is often called /etc/fstab or /etc/vfstab.
Sendmail Config Files If anyone works with sendmail, back these up for sure. If mail breaks, the quickest recovery is to restore from the backed up config files. These would be /usr/lib/sendmail.cf, /usr/lib/sendmail.fc, and /usr/lib/sendmail.mc.
Inetd Configs This file has been known to get misconfigured and is a target for hackers. This is the file /etc/inetd.conf.
TTY settings If you have any specialized devices attached, these should be backed up. These settings are typically found in /etc/inittab, /etc/ttytab, and /etc/ttys.
Start Up Scripts Any special scripts that get started at boot time should be kept in another area. These files would usually reside in the /etc/init.d or /etc/rc#.d directories.