I had a 133MHz Pentium system with 32MB of RAM that finally died last year. It was running a minimalist install of Ubuntu and was quite usable. I used PekWM as the window manager (very low memory consumption) together with fbpanel. Apps that were usable on that system included SIAG Office, Abiword, Gnumeric, Dillo, xcalc, xv, etc... I used XFiler (from SIAG Office) for my file manager. I suspect Xfe would have worked as well.
Vector Linux Light, as configured, won't run well at all in 32MB. It can, however, be modified into an even lighter form that will work.
On my Toshiba Libretto SS-1010 with 64MB all of the above run well, as do Xfe, Adie, Pathfinder, and hv3. Current versions of Abiword and Gnumeric are considerably heavier than the ones I was using a year or two ago. SIAG Office is better but Abiword and Gnumeric are still usable. Opera runs but it is very, very slow. My OS: VL 6.0 Light beta 2, desktop: JWM. pcmanfm is now disabled; it works but it tends to be slow.
Joe1962 pointed out that VL-Hot works without X. It will still automount a USB device or a PCMCIA card. It just won't pop an icon up onto the screen without pcmanfm. Unmounting has to be done at the command line. I'd bet someone could make VL-Hot work with xtdesk (used by Damn Small Linux to manage desktop icons) or even dfm. That would be considerably less resource intensive than pcmanfm.