Longest winning run

William Steinitz won 25 games in a row between 1873 and 1882. He won his last 14 at Vienna 1873, 2 against Henry Blackburne in the playoff, 7 against Blackburne in a match in London in 1876 and then his first two games at Vienna 1882. Mackenzie brought an end to the streak when Steinitz two pawns up allowed Mackenzie to escape to a draw by perpetual check.

The second longest run is Bobby Fischer's 20 game streak in 1970-1. He won his last 7 at Palma de Mallorca Interzonal 1970, won six straight in his quarterfinal candidates match against Mark Taimanov at Vancouver 1971, another six straight in the semifinal against Bent Larsen in Dallas, and then the 1st game of the Candidates final against Petrosian in Buenos Aires. Petrosian won the second game when Fischer came unglued in an extremely double-edged line of the Gruenfeld defence.