Ensure good physical security for computers, network cables, and connectors.
If user quotas are available on your system, enable them.
Configure appropriate process and user limits on your system.
Don't test new software while running as root.
Educate your users on polite methods of sharing system resources.
Run long-running tasks in the background, setting the nice to a positive value.
Partition disks to isolate critical partitions from those that might be filled by mail or file uploads.
Configure disk partitions to have sufficient inodes and storage.
Make sure that you have appropriate swap space configured.
Monitor disk usage and encourage users to archive and delete old files.
Consider investing in a network monitor appropriate for your network. Have a spare network connection available, in case you need it.
Install a firewall to prevent and react to network problems.
Keep an up-to-date paper list of low-level network addresses (e.g., Ethernet addresses), IP addresses, and machine names available.
Enable SYN cookies if your kernel supports them.
Use egress filters on border routers to prevent spoofed packets from being sent out from your network.