I want to have a web site into which I can put text documents,
possibly including images. Each document is a topic. People should be
able to comment on the documents. There should be a way to search for
documents. I should be able to organize documents according to various
categories.

This sounds almost like a blog, but I'm not really sure. Anyway what I
want is a tool that lets me create this easily, and add new text
documents easily. That is, I just want to enter documents, not really
spend a lot of time maintaining the client/server portions of the
software.

Finally, I want this to be stored somewhere that I can backup, not
only stored on someone elses web site.

I do run a web server, so some application that creates a bunch of web
pages in my own web tree would be ok.

I could create web pages myself, but I wouldn't get the commenting and
indexing functionalities.

-james

This is a possible solution to your problem.  Wikis are used for a
multitude of things, from FAQ to product manuals.  The pages can be
created and categorized under topics, as requested.

http://wiki.org/wiki.cgi?WhatIsWiki

As for backups, I would imagine any hosting service allows you to
backup your content and then download it (cpanel and ensim both do).