There was no single compelling reason for this. Instead there were many minor advantages that together pushed me to adopt it. Small annoyances would arise. I wanted to add Chinese characters [Chinese characters dictionary] [English-Chinese dictionary] to some of my pages, and also Unicode curling quotes [ in HTML]. Some of the other characters look useful. Unicode is the rapidly becoming the dominant standard: even Windows uses it now. It is also far superior to the old way, i.e. dealing with a myriad of mutually incompatible character encodings. Every programmer ought to know about Unicode.
Migrating the server was easy. A minor tweak in a configuration file (AddDefaultCharset UTF-8 in srm.conf for Apache), and changing XML headers was all that was needed.
First I reconfigured the Debian locales package (i.e. dpkg-reconfigure locales) and selected en_AU.UTF-8.
Next I checked if the programs I frequently use can handle UTF-8. Unfortunately for me, Eterm does not support Unicode.
After a brief investigation I settled on rxvt-unicode (aka urxvt). I miss some of the Eterm eyecandy, and it took me a while to supply command-line options to get urxvt looking like Eterm. On the other hand, urxvt is leaner, especially when run in client-server mode.
One minor inconvenience is that "TERM=rxvt-unicode" is not entrenched as it should be. For example, the dircolors supplied in Debian does not know about it, so either a custom file has to be written, or dircolors has to be fooled.