I have ubuntu running on an old laptop with specification of Pentium II
(333MHZ), 192MB RAM, and 6GB Hard drive.
It runs ok albeit in a not very snappy fashion.

Once you get a low level spec i.e RAM of 128MB or slightly less it is worth
taking a look at xubuntu
http://www.xubuntu.org/

As this is designed with low spec hardware in mind.