Slackware is the first UNIX-like operating system that I used, ever!, before being able to afford running Solaris on a Sun workstation and that happened 1994 or 1995, approximately. I remember FTPing the Slackware repositories to download all of the floppies Slackware was made up of. I don't remember how many but they were a good number. There were no broadband at home, at those times, and I had to download them at the University, write the floppies and bring them home, hoping they still were OK. Eventually I started buying the CD, but that was after having a CD-ROM.
I've been faithful to Slackware for a long, long time. At the end, I dropped GNU/Linux in favor of Solaris, both at home and at work, and did it with a bit of sadness. I got so used to the Slackware operating system that dropping it was really painful. Still nowadays I really feel like testing the new releases, and that's what I'm doing with Slackware 13.0.
Booting Slackware, for me, always tastes like a "Welcome back". The Slackware experience is peculiar. First of all, it's still a you-can-do-it-yourself kind of operating systems. The feeling of simplicity and cleanness that Slackware brings to the admin is remarkable. It's like you know where things are and where you've got to start for tweaking. And if you don't know, it's pretty easy to discover. Slackware guys, indeed, always try to brings unmodified packages from upstream: hence the very low distribution-specific pollution. If you wanted to read the manual of the software you're configuring, running Slackware you won't have any surprise.
The Slackware crew have been doing a great job and there always are great improvements from one release to another. But, as it's the case with distinctive brands, changes and improvements never break the Slackware way. That's of the things I love most.
Why should you install Slackware? Well, I usually suggest to give Slackware a try and then decide. Slackware's rock solid and, although the update process is not automatic (sorry, no Synaptic here...), you can update your system with packages from the development branch if you want to run newer versions of a package. The install process might be a newbies stopper: if you don't feel like running en Expert install and choosing packages one by one (it can be a pretty long process), you can simply perform a full installation and then free some space removing internationalization (*-i18n-*) and localization (*-l10n-*) packages, such as KDE's.
One of the most importante changes is probably the support for the amd64 architecture. Before, the only choice was running Slamd64, an unofficial port. The Linux kernel shipped with Slackware is version 188.8.131.52. Free to compile your own, as usual, but beware that kernel 2.4 support has been dropped and a version 2.6 kernel is now required. Slackware comes with its huge installation kernel and a choice of smaller ones for post-installation setup. If you don't feel like testing which kernel best fits your needs, you can install the huge kernel used during installation. Slackware release notes also suggest running the SMP kernel even in machines with 1 CPU.
As far as it concerns the desktop environment, you slackers know that Slackware isn't shipping nor supporting GNOME. Slackware 13.0 brings the new KDE 4 Desktop Environment (v. 4.2.4), which finally has reached a point in which it seems mature for the regular users. And if instead of KDE's eye-candy you'd rather run a light and GTK2-based desktop, there you have Xfce.
HAL and udev integration has been there since a couple of releases and nowadays Slackware is a perfect choice for the desktop of the casual user. No more su and mount just to use a pendrive.
Slackware doesn't come with libdvdcss, which you're going to need if you want to reproduce encrypted DVDs. But don't worry: just download the source package, ./configure it and it'll build perfectly.
Xorg has been updated too and chances are you'll be running your X Window System without even setting up a xorg.conf file. Slackware kernels include DRI support and, if you've got a suitable card, you'll enjoy hardware acceleration out of the box.
If you want to read the release notes with all the details, here it is.
Many years have passed and Slackware is always there, faithful to its design principles, rock-solid and as clean as ever. Should I run Linux, I'd choose Slackware. If you need packages you can start from Linux Packages or SlackBuilds. Furthermore, as far as I can tell, Slackware is one of the best distributions to compile software: the complete install comes with everything you need to compile most part of the packages you'll ever need which are just a (./configure ; make ; make install) step away (well, you'd better build a package before installing).
Great work as usual, Slackware crew.