Perhaps one of the best Linux distributions tailored for older hardware is DeLi Linux. It’s simple, and performs well enough to run on hardware as old as a 486.
In fact, DeLi Linux runs on anything better than a 386 with at least 4MB of memory, though if you have only 4MB, don’t expect stellar performance. Things get decent at 8MB, 16MB is smooth, and 32MB or more is perfect. I tested DeLi Linux on several machines, ranging from a 66MHz 486 DX2 with 8MB of RAM up to a a Dell Pentium III system with 256MB of RAM. The 486 system struggled to open anything, taking several minutes if things got too complex, such as when I was running a window manager, the X server, and AbiWord. However, DeLi Linux surprised me by turning the old 486 into an usable system, provided I had patience to spare. What’s more, the Pentium III was extremely responsive, being even faster than my main AMD64 system running Fedora Core 6.