Anybody knows webmail applications, but there exist a whole lot of webbased applications that you can run on your own server/desktop-with-webserver. Of course a whole bunch of CMS's, Forums, weblogs etc, but I want to highlight some more exotic ones.
First, I use Sitebar since July last year. Sitebar is an online bookmarking tool, which can sit in a sidebar of your favourite browser, or just in a tab of it or whatever. Anyway, you can integrate it in your browser if you want, import your existing bookmarks of all those great pr0n^Wgadget sites and have access to your bookmarks wherever you have access to your webserver. It's written in PHP and is a real gem if you like collecting links and actually find them back.
Secondly, there's Zoë. I discovered this gem only recently [read: today], but it's already digging my e-mail archives. So what is it? It's "google for your e-mail". It indexes your e-mail folders and presents a nice web frontend, which you can query in lots of ways. Find all e-mail of your birthday last year, all mail from your lover or your work. Whatever. It works just like Google. It's written in Java, and can reside on your desktop or your server. It can act as server itself [indexing your sent and received mail immediately], as client [POP3, IMAP], or just can import your mboxes. Very, very neat.
Lastly, I can recommend AWStats. If you have a webserver and like statistics, this program is made for you. It's a nice piece of Perl script which digs your Apache logs [or even your ftp or e-mail logs] and presents it in a nice way, including graphs, reverse lookups of domains, what browsers people used and what search keys people found your site with [very, very interesting, as people are really weird considering how they find my websites :)].
Just a note that I'm not affiliated by any of these projects. I just like them so much that I wanted to highlight them, and maybe create a Better World(tm) for somebody out there.