Q:

Improving worldwide website performance without using a CDN? 

CDNs seem like a tremendously brute-force approach to improving website performance across the world, since they use some thousands of machines close to the end-user to ensure good throughput. 
Are there any ways of improving performance over long distances with high latency or slow-ish links (e.g., UK to Australia) over the "usual" methods of reducing size and number of requests, or is the only other way to have servers closer to the user? 

A:

You can't circumvent latency by reducing size.  Just make sure your server supports Keepalive, everything that should be cached actually comes with appropriate Expires: headers and that your HTML is reasonably sized (i.e. also use gzip compression) - then see how far you get with that and whether multi-homing is still necessary.