@haywire: I use Vector 6.0 light on 700 MHz Coppermine laptop with 128 MB RAM. Works great! Idles on 40 MB RAM. Rarely ever uses SWAP. I presume that nightflier is right re. 64 MB setup.
The only other usable Linux for my old laptop machine was Salix LXDE (60 MB RAM "idle"). However, Vector is faster. I would like it upgraded a bit to newer kernel and ext4 filesystem so I can use it on other machines as well.
Please beware that modern popular apps like OpenOffice and Firefox might take 50 MB of RAM. So, do not even think of trying on such a low mem computer. Do not waste time on any of the lighter flavors of any other distro! Nothing will work. DSL will as well as well as DELI but you are looking at distros no longer developed for years (At least no updates published). Puppy will NOT work. You will be able to install it, bur apps will take A LOT of RAM. (PET intaller takes 200+ MB).
Antix will be taxing 60 MB of RAM. No use either.
So, it is either Vector Light or X-less system. BE CAREFUL: when upgarding apps, CHECK the dependencies. It often attempts to install Gnome dependencies that you do not need (It will want to install Nautilus etc). So, before the actual upgrade, "uncheck" whatever is related to Gnome.