Hmm what can typically go wrong.....
1. server being compormised
2. server being spammed/relayed off
3. chance of hardware failure is small. But heck it happens sometimes especially to fans.
What you can do to prevent trouble
1. make sure your server runs logrotate if its a nix box, or clean up the logs in /var once every week. Or use logrotate to rotate the logs automatically by time/date or by size.
2. always remember that a server is your baby. That means going in and routinly checking everything on a sechduled basis. logs, bash, if it is redhat based, do a rpm -V on main utilities such as fileutils, procps, etc.
3. put up a firewall. Use iptables extensively. (if nix)
4. make sure all announced vulnerabilites are patched on a regular basis.
5. Do not give out root access to lots of people. Perferably 1 or 2. There is bound to be some dummy who will accdidently mess up soemthing.
6. SSH all the way.