Okay, I finally knuckled under and decided to add tags to my theme. Prior to WordPress version 2.3, you had to use a plugin in order for your theme to support tagging. Now, however, it's a native function and it's pretty easy to use. If you look down at the bottom of this post, you'll see "Categories:" followed by "Tags:". It's going to take some time to go through a thousand other posts to add tags.
You may wonder why I'd even bother to start using tags this late in the game. It's the related articles thing. I was maintaining a separate database to keep track of related articles, using keywords. Kind of like tagging (duh). Once I thought about it, I decided to stop circumventing the plugin that shows related posts and just add tagging. It'll be a whole lot easier.
I already had both an archive.php and a category.php file for my theme (that I previously copied from index.php and modified). I just added a tag.php file to the list. As soon as I make a couple of minor changes, I'll be all set.
Just in case you want to play with tags, and the theme you're using doesn't support them, take a look at this WordPress Codex page to make sure you're doing it right: Template Tags/the_tags


