Paul Keres (17.01.16 - 05.06.75) was a top-class grandmaster, the strongest player never to have played for the world championship title. In fact after his first place in the 1938 AVRO tournament in Holland he was regarded as the natural successor to the reigning world champion Alexander Alekhine.
At the AVRO tournament in 1938 Paul Keres was the only undefeated player and finished in first place, ahead of four world champions (we count Botvinnik as a future world champion). Keres beat nine world champions during his career, including Tal, Smyslov, Petrosian, Spassky and Fischer, some of them several times. He was the most consistently successful player and won more international tournaments than any of his contemporaries. He won the USSR championship three times and played in ten Olympiads, achieving an amazing overall score of 80%.
The reason that Keres never played for the crown is shrouded in mystery. He participated in eight candidates events and came second in four of them. The turmoil of World War II and the annexation of his small country Estonia by the Soviet Union certainly played a role in keeping him from reaching the very top. Keres had participated in German tournaments during the war, and when the Red Army liberated the country, Soviet authorities planned initially to execute him. Botvinnik interceded by talking to Stalin and Keres was spared.
In Estonia he received a state funeral, with over 100,000 people in attendance. His image was put on a postage stamp, and the National Bank of Estonia issued a five krooni bank note with a portrait of Paul Keres (unfortunately cropped by chess.com despite all my efforts to include the full image, from the source below - NR) This has not been done for any other chess player in the history of the game, as far as we know.