In the 1950s and 1960s Stefan Kapłaniak was one of the best kayakers in the world, winning medals at the World Cup, European Championships, and Olympics, along with multiple Polish titles. Kapłaniak made his breakthrough in 1950 when he became the Polish junior champion. From 1953 to 1968 he won 30 national championships including multiple titles in the K1 500 metres (1954–59, 1961, 1964) and the K1 1,000 metres (1956–59, 1961). During this period he had his greatest success when he won gold at the 1958 Canoe Sprint World Championships in the K1 500 metres and K2 500 metres, winning the latter with compatriot Władysław Zieliński.
Kapłaniak won several medals at the European Championships, with his first coming in 1957 with bronze in the K1 500 metres. Two years later he won gold in the same event, followed by silver in the K2 500 metres in 1961. At his first of three Olympic appearances he finished fourth in the K1 1,000 metres at the 1956 Melbourne Games. Four years later Kapłaniak and Zieliński won bronze in the K2 1,000 metres at the 1960 Roma Olympics. The pair teamed up for the 1964 Tokyo Games but were eliminated in the semi-finals. Kapłaniak was honoured with multiple awards including the Distinguished Master of Sports, the Gold Cross of Merit, and the Medal for Outstanding Sports Achievements.