The best replacement for slackware is debian.

The best alternatives to slackware are rated as following:
★★★★★  debian
★★★★★  gentoo
★★★★  arch
★★  fedora
★  freebsd
★  centos
★  arch linux
★  redhat
★  suse
  backtrack
  slax
  openbsd
  archlinux
  crunchbang
  mandrake
  linux from scratch
  red hat

Your alternative for slackware is not listed? Suggest!
Speaking about slackware, one probably shouldn't forget about grub.

Other search terms related to slackware and their ratings are:
★★★★★ grub
★★★ lilo
You have in mind a companion for slackware and it is not yet here? Propose!



Google Trends

Scale is based on the average worldwide traffic of slackware in all years. Click on graph for more.
slackware
debian
gentoo