I'd always assumed that Red Rubber Ball was written solely by Paul Simon, but the wikipedia entry for the song credits Bruce Woodley of the Seekers as a co-writer. The song wasn't recorded by Simon and Garfunkel aside from a live version which I'll feature here. It became a 1966 hit for The Cyrkle.
Here's the live version by Simon and Garfunkel:
Here's the hit version by the Cyrkle:
Finally, here's the version by one of my favorite bands of all time, the Australian folk group The Seekers: