WordPress is the the leading blog engine right now. I've been using it for years and am pretty comfortable with setting it up on a webhost, but what if you want to play with it for a while and don't have a webhost or just want to keep your bloggy creations off the Internet? Simple, you download everything you need and run a complete server on your own machine. Have 30 mins? That's pretty much all you need, so let's get going.
Despite my general Mac bias, Macs do have an edge in the whole "run your own server" department because, well, OS X is built on UNIX and that's essentially a server OS out of the box. So, from TUAW and dg.labs two simple sets of instructions using MAMP (this is what I use and have my students use as well). For PC users, XAMPP is the way to go and via WordPress.org here is a simple tutorial on getting XAMPP going for yourself.
Once you have MAMP or XAMPP installed you could move from WordPress to
Mediawiki or even (gasp)
Drupal! Sure this is a step up on the geek-o-meter, but hey it's fun to try things like WordPress on your own.
Come on, get serving!