I think this could be defined into two categories, things with CLI only, and things that can run a reasonably modern GUI.
In the first category you'd have trouble finding a modern linux kernel for 32-bit, and distro, that is actually "i386". Since most things long ago dropped support for CPUs that don't have the i586 extensions and things like MMX/SSE. The 32-bit kernels you can get now, as far as I know, require at least a P166MMX or better to function properly.
In the second category, you need something with enough CPU and RAM resources to run a barebones xorg + openbox desktop environment, or xfce, or lxde, or similar. And then the ability to run a browser and terminal applications.