Tiny Core Linux is one of the smallest and fastest distro with a graphical user interface (GUI). It has an application manager to install application by just a few clicks.
What are the minimum requirements?
An absolute minimum of RAM is 46mb. TC won't boot with anything less, no matter how many terabytes of swap you have.
Microcore runs with 28mb of ram.
The minimum cpu is i486DX (486 with a math processor).
A recommended configuration:
Pentium 2 or better, 128mb of ram + some swap
More info and download at: http://tinycorelinux.net/