People here might know him best for the "Game of Life", but he did so much more. The book about Conway by Siobhan Roberts is an interesting read about the man and his work.
Some will know Conway via is work on the Classification of Finite Simple Groups (with *many* others), some via his "Look and Say" sequence, while still others will know his book "Winning Ways", written with Richard Guy and Elwyn Berlekamp. My copy signed by all three is something I treasure.
@ColinTheMathmo RIP. There are few mathematicians who's names crop up as often in as many different contexts and fields as Conway's. Discrete mathematics has lost a giant, but he certainly left some wide shoulders to stand on.