Log Locally and Remotely with rsyslogd

It looks like it's as simple as two lines in the config file:

*.* @loghost
*.* /var/log/messages

The rsyslog example configs have a few instances of teeing like this. The key one:

kern.* /var/adm/kernel
kern.crit @finlandia;RFC3164fmt
kern.crit /dev/console
kern.info;kern.!err /var/adm/kernel-info

The second statement directs all kernel messages of the priority crit and 
higher to the remote host finlandia.
[...]
The third rule directs these messages to the actual console, so the person 
who works on the machine will get them, too.

Wouter de Bie had a good answer, but he showed the UDP method of sending logs. In order to send them over the more reliable (though not 100%) TCP use something like:

\*.* @@remote.server.ip

Put the following line in your /etc/rsyslog.d/remote.conf:

*.* @remote.server.ip

This can easily be extended for only logging specific facilities and levels to the remote server.