Reversi

Reversi - invented in 1883 by either of two English men (each claiming the other a fraud), Lewis Waterman or John W. Mollett (or perhaps earlier by someone else entirely).
[wikipedia]

Now you can play it for free - with your friends or against someone else entirely.
If by some twisted fate you happen to be the only survivor of a Zombie Apocalypse - you can challenge yourself against three different levels of AI.