Marcos did a nice resume of common points of MAINTENANCE: monitoring, backups and updates.
I need to repeat (by people comments) that monitoring != maintenance.
I would like to add: cleanups of old users, old cron tasks, etc. Passwords renewals. Evolution of system configuration (looking at monitoring history) (and this includes evolution of monitoring and backups) with the life changes of the server. Security audits. Custom reports (i.e. detailed usage of services, shared resources, security reports). And...
Restore backups randomly (without needing to do it). Also always include a copy of the MBR (Master Boot Record) if you do not use an automated deployment system to restore the whole server.
I've seen firewalls survive 500 days of uptime (yes, that is a BAD maintenace, because there are about 10/15 kernel upgrades a year, so big uptimes, use to be equal to vulnerable kernel) without any human maintenance. It's just a good config on partitions, syslog and no major configuration changes.
You ask for scripts. Maybe there are generic pre-packaged scripts, but it is more about DIY (Do It Yourself). So first you learn or read how your system works (this includes distro specific REAMEs, man pages, policies and compilation options), then yo think how your system should behave, and then you write custom scripts (cron, custom commands, etc) to manage the combination of O.S. + desired behavior/results/reports/change-management/rollbacks/reactions/etc.
Also, available generic tools (monit, nagios, cacti, zabbix, etc) can be extended with your scripting skills and available third party plugins.
In example: do you need only to know "if partition is full", or do you need too to control disk temperature, free inodes, files and folders rights, checksums, S.M.A.R.T. status, bad sectors, filesystem checks, and estimated life cycle of physical hardware?
And as well as the backups, the monitoring system + customizations, should be validated where possible, simulating failures, attacks, etc.
Custom scripts are better, when you can validate them and clean bugs, on a pre-production server(s), environment, directory, database, etc.