Well, that depends entirely on what you wish to use it for...

I've ran many P1 linux boxs... and they are still usable..

Linux cares more about ram then it does CPU.. so having as much ram as you can lay your hands on will be a big bonus.

If your planning on using an old P1 system as an internet gateway router.. thats great.. and there are a ton of them around..   take a look at this one:
http://www.devil-linux.org
for starters.

If your looking to use your P1 as a desktop workstartion etc.. then the task is much harder..
(because the GUI's are some of the most ram/cpu hungry apps on linux)
Your best bet is an older linux distro.. like mandrake 7.0 or  Redhat 6.2 etc....

A linux designed for your system is going to run much faster then one designed for Athlons and P4's if you get my meaning..

If you go to this page:
http://www.mandrakelinux.com/en/ftp.php3
(say you are already a member of the club at the prompt for now)

You will see a listing for "older versions of mandrake"..
getting hold of a copy of Mandrake 7.0 would probably be perfect for running on that system.. but if its a 233mhz and you have at least 64MB of ram in it, you could go for something much newer.

regards

Franki