Don't throw that old computer away just yet. MEPIS let the word out yesterday about AntiX, a community-developed derivative of MEPIS 6.5 that will work with machines with as little as 64MB of RAM.
Read it here
AntiX is recommended for machines with 128MB of RAM, but will also work with machines with only 64MB of RAM and 128MB of swap space. MEPIS will run with a minimum of 128MB of RAM, but not very well.