I just fired up my old Thinkpad (350 MHz, 64MB) do some testing.
It runs Slackware 11.0 (2.4 kernel).
free gives me (+/- buffers/cache):
51MB free - after booting to runlevel 3, no swapping
45MB free - after starting fluxbox via startx (=without a login manager), no swapping
29MB free - after starting firefox 2.0 with google open, no swapping
After opening two more tabs and opening linuxquestions and the german facebook-lookalike, it's at
23MB free, but 6MB of swap space used already. (Let's not talk about free now
Starting firefox took roughly about 30 seconds, by the way, and that's 2.something. Imagine starting some decent music player app like amarok now... And you really don't want to try youtube on that machine for sure.
I have never tried puppy. I can't imagine it performing much better though.