Slackware has a similar system to apt-get, its called swaret, and in my experience, it worked very well.
Swaret
Also, if you choose to not use swaret, pkgtool is very easy for installing/upgrading packages, you just have to download the packages yourself. Packages can be easily found on
www.linuxpackages.net
Contrary to the name, its mainly slackware packages.
You should also check out
Gentoo for really-up-to date package management while retaining the ease of use of apt-get and swaret, except done better, though its a little harder than slack or debian, as far as the installation,etc goes.