Simplicity (not to be confused with ease of use) and stability. Slackware's one of the easiest to understand distros around, from the boot sequence to service and user management.
Not much is done for you, but nothing is hidden from you. As such, it takes work, but it rewards the user with the feeling of knowing the full system.
Rock-solid stability. Even running the -current (development) version, I've not seen any show-stopping bugs. The bugs I do see are all upstream, and are patched quickly by Pat and the Slackware team. If you are masochistic and enjoy the sometimes daily breakage of distros like Arch and Fedora Rawhide, you won't get your jollies here. But if you want a stable, fast, sysadmin-friendly OS with no surprises or NIH nonsense, give it a shot.
Speaking of patching, Slackware tries to stay as close as possible to the upstream developer's version of a package, with minimal patching. Patches are usually security related, and sometimes a package is patched to fix a bug found in testing, but there are no exotic tweaks like what you get with Ubuntu and other "flashy" distros.
Package management is as simple as it gets; there is no dependency resolution so the user is responsible for making sure they have everything they need for a particular package. Personally I prefer this approach, it reduces bloat and puts me in control of my system. That said, it's not for everyone, and there are some third-party package managers that enhance the existing system with dependency resolution and a pretty interface. You can also build from source just about any package you want to, as Slackware includes a complete dev toolchain for the most popular languages, and you can easily install support for less popular ones.
There is no systemd, which to me is a blessing as it makes for much easier and more familiar management.
Obviously I'm a fan, but there are some downsides I'm willing to admit. It's not flashy; the various desktops that come with it (KDE, Xfce, Fluxbox, Blackbox, WindowMaker, fvwm, twm) are bone-stock with no customization like you get with other OSes. This means a ton of tweaking on the user's part if you don't care for the default themes.
GNOME support is nil. Pat dropped GNOME in the mid-2000s when he got frustrated with building it, and while there are third-party solutions, none of them work 100% in my testing.
Unless you run -current, the stable version tends to get left behind. It's been nearly three years since 14.1 was released, and it was clearly showing its age, though some would consider that a good thing (I certainly do, especially for servers, which is what I use Slackware for on two systems).
There is no systemd, and for many people that makes it a non-starter.
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I say, give it a whirl. You may be pleasantly surprised! Then again, you may run screaming back to your bells-and-whistles eye candy OS. But at least you can say you tried it. :-)
"Speaking of patching, Slackware tries to stay as close as possible to the upstream developer's version of a package, with minimal patching."
Posting this from my Thinkpad X220 running Slackware 14.1.
Just check config files (*.new suffix) when a package is updated to a newer version. Debian/CentOS backport patches to packages so that the configs don't change during a release.
Quite happy with what I've had from Slackware for the past couple of years and I have subscribed. The distribution does not pretend to cater for all needs but can support many use cases.
Remember that there is now a live iso image to try before you install.
I find that it aligns very closely with OpenBSD; users familiar with one will soon be comfortable in the other. Slackware is by far the most BSD-like Linux distro.
I used to run it, and I'm not sure there's value in it anymore. They often don't stay on top of security updates, and compiling anything just got worse and worse.
The last straw was the fanboys at the linuxquestions forum. It was cultish and creeped me out.
Three negative comments on this submission, that's some impressive anti-cult thing you've got going.
Slackware doesn't do "security theatre" updates. Whenever there's both a credible risk and a reasonable fix, you'll see an update, and it'll be quicker than distros that are multiple steps downstream from Debian.
You know, I felt really troubled to have been using something for 20 years and realize things had changed and it was no longer right and no longer good for me. I felt like a fool for having stuck with it for quite so long.
I realize that sounds like someone talking about a bad marriage, and I suppose we can generalize usefully on relationships of whatever type.
I think we must end up with longer-lasting bad feelings about anything we used to value.
Not much is done for you, but nothing is hidden from you. As such, it takes work, but it rewards the user with the feeling of knowing the full system.