Software running on

Secure MTA (mail transfer agent). The widespread sendmail (the beast) is way too dangerous. Qmail is nice too but I favor Postfix because it is free software, the rest of the MTAs are no match (especially because their security is fundamentally flawed: large monolithic binaries running as root).
ejabberd is a fault-tolerant jabber server, supporting distribution. Written in the erlang language. The best free software jabber server.
Dovecot imapd
Less bloated than Courier-IMAP, and of course it uses maildirs. In the past I used Binc IMAP, but dovecot supports caching (speeds things up considerably).
The most common webserver. Lighttpd crashed quite often and php4-cgi consumed 100% CPU power every once in a while, so I moved back to Apache. This time with SSL provided by mod_ssl, so that there's only one apache daemon running.
Iloha Mail
Faster than the popular Squirrelmail because it has caching and doesn't do a new IMAP login all the time.
Secure shell and file access. And port forwarding.
Caching http proxy, features pipelining, keep alive and other features to make browsing faster.