First of all, I apologize for all the great players left out (Marshall, Spielmann, Maroczy, Timman, Shirov, etc) but I had to draw a line somewhere. Besides, that's why I left an option for "other...."
With all the talk about greatest player or greatest book, I thought it might be time for a greatest non-champion.
When I was first learning chess I read many times that Keres was considered the strongest by several great soviet champions. There seems to be a feeling that Keres was of equal strength but just never had a good run when he needed it.
Some, of course, argue Rubinstein was the best player in world for several years (before the war) and would have given Lasker a good run for his money (which is saying something...). Personally, I think Korchnoi, who was a hair away from beating Karpov and has played strong chess for 40 years, is an excellent candidate and my personal choice.
Nimzowitsch and Tarrasch had a huge influence on the game and Ivanchuk would probably have been champion several times over had it not been for the K's of the 80's and 90's.
Anyway, I'm curious what other people think about these great players.