1. There's no package management system.
Yes, you heard right, but hear me out...
Slackware has a package system. It's packages ending in .tgz Other package systems are .deb and .rpm. The package management system is Synaptic/apt-get for Debian, Yum for Red Hat, Urpmi for Mandriva, and so on. Slackware doesn't have a management interface for the packages, you have a couple of scripts to slap things in and then you're on your own.
Now, it's true that the package management interfaces on other systems are nice. But let me install about my twenty-fifth package and do my second upgrade, and the whole system is hosed up. Then I have to manually go in and fix stuff, except - oh, barnacles! - the system wasn't designed for mucking around in its guts! Slackware starts you out with you getting your hands dirty, but doing your own package management means you know exactly the why and how of everything down to the last byte. So once you've done it, you've done it right and never have to worry about it again.
2. Slackware isn't for slackers.
Slackware demands perfection. If there's a tiny little thing wrong anywhere, Slackware lets me know, and keeps nagging me until I have fixed it. It is consistent. Other systems try to do too much of the driving for me, which I wouldn't have a problem with if they never went wrong. But they do.
3. There are no clueless Slackware users.
Which means that when you need help, you can get it quickly. Post in a forum or chat where Slackware is the main topic and get an answer right away. "Anybody remember that Lisp predicate to have Emacs check whether it's running in the console or in X windows?" "(eq window-system 'x)!" "Thanks!" It's over that fast. Everybody knows they're on approximately the same level, so it just saves time.
4. Slackware is silly putty.
You can mold it and shape it from the ground up. This is actually true of any major Linux system, but with Slackware it's built with the assumption that you'll want to customize things your way, and then it gets out of your way and lets you do that.
5. Slackware has Dropline.
The Dropline Gnome project is an install for Slackware. When I first got Slackware 11.0, I was a little put off at Gnome not coming with it. But I am glad I stuck with it, because now that I've put in the latest kernel and put in Dropline, I've discovered that Dropline is one powerful package. It not only installs Gnome, but upgrades the whole system in one round shot. In the end, with just two stops, I ended up with the same setup that I would have had to dribble in one apt-get at a time for three months on Debian.
6. Slackware isn't destroying itself for the sake of converting five more Windows users.
What? I had to say that; give people something to flame about...
Slackware is unapologetic for being Linux. It is hardcore Linux with a sharp flavor of classic Unix and some BSD packages thrown in for good measure. Now, I know all the user-friendly minions are shambling to my gates to lob stones at me already, but I have just as much right to what I want as you do. I'm just as glad as anything that there is Ubuntu, Mandriva, and Knoppix for the new Linux user.
But sometimes, I would like a bike WITHOUT training wheels welded onto it, because I don't mind sacrificing a little safety for the sake of feeling the wind in my hair. Linux distros as they stand today are 90% dulled down so the new users don't hurt themselves. For experienced users we have about five distros left that haven't had the bad words bleeped out... the bloody scenes cut... the script and soundtrack remastered to appeal to the marketing department's favorite demographic... the story simplified and the punchy lines taken out of the dialog to shorten the running time to fit the limited attention span. That's it, about five distros that haven't been blended to a smooth puree. People really should try chewing their food again - it actually does taste better that way!
7. Slackware hovers at about the number 10 ranking in Distrowatch's popularity.
So when people like me say Slackware is their favorite, you know it isn't just somebody doing it to say "Me too." It's low enough in ranking to need a little rooting for the Underdog. And yet - it is, indeed, hovering! Steady. As opposed to some of the other distros, which bounce up and down like a NASDAQ stock the morning after a Silicon Valley arrest. It must be doing something right.
UPDATE: For those looking for links about Slackware (now that somebody asked):
The Slackware Home Page
Mad Penguin's Documentation project
Slackware Package Site
Handy archive of Slackbuild packages
My own review of Slackware 11.0 when I first got it, includes links to Dropline and a kernel-upgrade tutorial
UPDATE: Perhaps the best meta-link of all, Béranger has a flock of Slackware-related links, and a six-pack of Slackware-related opinions on the rest of the site to go with them. Flaws in Dropline are discussed elsewhere on the site, which don't impact me as I'm a Fluxbox-type who only needs the Gnome and KDE systems for package support.