José Raúl Capablanca famously went eight years without a loss (1916 to 1924, including his World Chess Championship 1921 victory over Emanuel Lasker), but this was "only" 63 games.

 

Between October 23, 1973, when he lost a game in a Soviet championship, and October 16, 1974, when he lost to Kirov at the Novi Sad tournament, Mikhail Tal had a string of 95 tournament games without a loss (46 wins and 49 draws). Tal also has the second-longest unbeaten run in top-level competition. He went unbeaten in 86 games from July 1972, when he lost to Uusi in the tenth round at Viljandi, until April 1973, when he lost to Balashov in round two of the USSR Team Championship in Moscow. This streak included 47 wins and 39 draws.

World Champion José Raúl Capablanca 1926