<p>I have a classic client/server (fat client and database) program written in Delphi 2006. When certain conditions are met in the client, I need to notify all the other clients very quickly. Up until now this has been done using UDP broadcasts, but this is no longer viable as clients now connect from outside the LAN and the UDP broadcast is limited to the local network. </p>

<p>I'm aware of the Indy libraries but am not really sure of which components to use and how to structure it. I'm guessing I'll need to have a server that the clients connect to which will receive and distribute the messages...? Any samples out there to get me started?</p>

<p>Are there any other component sets or technologies I should look at instead/as well?</p>

You should be able to use Multicast UDP for the same purpose. The only difference will be to join the multicast group from every client.
http://en.wikipedia.org/wiki/IP_Multicast
http://en.wikipedia.org/wiki/Internet_Group_Management_Protocol
Edit:
Just to clarify, multicast let you join a given "group" associated to a multicast ip address. Any packet sent to that address will reach every client who has join the group