Got my RPi on 2012-April-19. Currently running the customized Debian image, since I know a little more about Debian than the other supported distros (Arch, Fedora).
Slackware on the Pi
One of my project ideas will be to get Slackware ARM running on the RPi. I would think that the Debian kernel and modules, with Slackware ARM userspace, could be hacked together to work, but that's only an uneducated guess. Slackware ARM currently has three installer images, for the three supported platforms; I eagerly await the fourth, Raspberry Pi.
2012-05-02, late evening
I have a Slackware ARM setup that crashes in /etc/rc.d/rc.S. But at least that means /sbin/init is running from the flash card. Yay!
It turns out the SD card and my desktop's reader have some kind of conflict, and e2fsck's clean-up sent many critical libraries to /lost+found/. Another file that disappeared was /etc/fstab. Not good. My netbook's card reader works OK with the card, so I'm re-installing the libraries now. We'll see what else got clobbered, but the libraries are the most important thing to repair.
It works! My basic idea above (Debian kernel, Slackware ARM userspace), using the packages outlined here, has given me an RPi that works on the network. The installation is 291M (in a 1.5G partition), with DHCP, without X.
Now, to clean it up and find a way to get it online. Suggestions welcome for hosting/distribution; I can't host it myself.