Amounts of RAM

runs with 128 megs
------------------

Damn Small Linux (not really that small memory-wise)

runs with 64 megs
-----------------

Minimal Linux Live, 4.4.6 kernel

runs with 46 megs
-----------------

Tiny Core Linux 

runs with 32 megs
-----------------

Plan 9

runs with 16 megs or less
-------------------------

2.11BSD (running on 4 megs)

Basic Linux 3.5 (running on 16 megs, based on slackware 4.0 from 1999 and still active)
uses 2.2.26 kernel

MuLinux (run in 4 megs of ram with a hard drive)

Tomsrtbt (floppy based system)
uses 2.2.X kernel
needs 8 megs of ram to run
uses ash instead of bash for shell

AmigaDOS 1.3 (runs with 512k)

Unix Version 7 (runs on 256k but can use up to 2 megs of ram on PDP-11/70)
Unix Version 5 (runs on 256k)

window managers
---------------

icewm  4.5 megs