It's a bit tragic that he is remembered for something he himself wasn't very fond of. From his biography:
"Do you know something? I hate the Life game. I've really realized that I hate the damned Life game. ... I'm scared of the following thing happening. I'm scared of it becoming another one of these, 'John Conway, inventor of the celebrated Game of Life...' I told you, every time I turn to a book, a new math book, I look up the sacred name and it says: 'Conway, Game of life, pages 34 to 38.' And that's roughly all it says. And how can I say it---it's not character assassination, exactly, it's quality assassination. I regard Life as trash, and frankly. I mean, it was a real part of my life to have discovered it and so on. And I don't think it should be totally removed. But it seems to be all that I'm known for, among the general public. ... This was never a big deal as far as we were concerned. This was just a recreation, a game we played. Somehow it became a bit more important later on, or at least it did in the eyes of other people. I never thought of it as very important, I just thought of it as a bit of fun. In fact, in a way, I felt ashamed of it. I don't think it counts in the mathematical community, or at least in the serious mathematical community. I don't think any of my Princeton colleagues think this Life game is of any importance. I don't know. In a way it doesn't count for me."
I listened to the numberphile podcast on it yesterday where Brady interviewed Conway's biographer, and it looks like conway had come around to liking the game of life by the end. The real tragedy is that he never figured out the monster group
"Do you know something? I hate the Life game. I've really realized that I hate the damned Life game. ... I'm scared of the following thing happening. I'm scared of it becoming another one of these, 'John Conway, inventor of the celebrated Game of Life...' I told you, every time I turn to a book, a new math book, I look up the sacred name and it says: 'Conway, Game of life, pages 34 to 38.' And that's roughly all it says. And how can I say it---it's not character assassination, exactly, it's quality assassination. I regard Life as trash, and frankly. I mean, it was a real part of my life to have discovered it and so on. And I don't think it should be totally removed. But it seems to be all that I'm known for, among the general public. ... This was never a big deal as far as we were concerned. This was just a recreation, a game we played. Somehow it became a bit more important later on, or at least it did in the eyes of other people. I never thought of it as very important, I just thought of it as a bit of fun. In fact, in a way, I felt ashamed of it. I don't think it counts in the mathematical community, or at least in the serious mathematical community. I don't think any of my Princeton colleagues think this Life game is of any importance. I don't know. In a way it doesn't count for me."
Apparently his favorite work was on the surreal numbers: https://en.wikipedia.org/wiki/Surreal_number