Syslogd should already be running on your system; what you need to do is enable its UDP listening option. This is controlled by a section near the end of /System/Library/LaunchDaemons/com.apple.syslogd.plist; remove the comment markers so that it looks like this:
<!--
Un-comment the following lines to enable the network syslog protocol listener.
-->
<key>NetworkListener</key>
<dict>
<key>SockServiceName</key>
<string>syslog</string>
<key>SockType</key>
<string>dgram</string>
</dict>
</dict>
</dict>
</plist>
And then reload the syslogd daemon either by rebooting, or by running:
sudo launchctl unload /System/Library/LaunchDaemons/com.apple.syslogd.plist
sudo launchctl load /System/Library/LaunchDaemons/com.apple.syslogd.plist
UPDATE: Starting in OS X v10.7, Apple switched com.apple.syslogd.plist to a binary plist format, which doesn't include the relevant comment, and isn't editable as plain text. With the new format, PlistBuddy seems to be the easiest way to add the listener:
cd /System/Library/LaunchDaemons
sudo /usr/libexec/PlistBuddy -c "add :Sockets:NetworkListener dict" com.apple.syslogd.plist
sudo /usr/libexec/PlistBuddy -c "add :Sockets:NetworkListener:SockServiceName string syslog" com.apple.syslogd.plist
sudo /usr/libexec/PlistBuddy -c "add :Sockets:NetworkListener:SockType string dgram" com.apple.syslogd.plist
sudo launchctl unload com.apple.syslogd.plist
sudo launchctl load com.apple.syslogd.plist