8 MB is plenty to run Slackware in.
Check out the 4MB Laptop HOWTO
. I successfully installed Slackware 8.1 on a Compaq Contura Laptop (486/33mhz, 8MB of RAM, 270MB hdd), with PCMCIA support, and a working NIC. I got it done in under 100MB; it didn't include X, but it was a GREAT SSH client.