Administered networks often make use of a central Log Server to store the SysLog output of the local servers. This is also a good approach when setting up a Log Analyser or IDS.
To enable sending SysLog output via network for syslogd, simply alter it's flags in /etc/rc.conf. Use -R Host[:Port] to send all messages to Host, and Port (optional). To keep the messages locally also, give -L as additional flag.