the answer used to be "slackware" I suppose it may still be.
That's for machines with less than say 24M of memory.
I'm happy with debian on my boat anchors, but they aren't entirely memory-starved.
Slackware used to be proud that the "lowmem" install set would work in a box with 4M.
http://www.sunsetsystems.com/tip-lowmem.php3 is from 1999, but google indicated that a lowmem install is still part of 2004-dated slackware repositories.