The record as of 2015 for the most NBA overtimes goes to the January 1951 game between the Indianapolis Olympians and the Rochester Royals. The teams played through six overtimes.
The teams each scored one point in the first and third overtimes, no points in the second and fourth overtimes and four points each in the fifth overtime. The Olympians won the game with two points over the Royals in the sixth overtime. The final score was 75-73.
The matchup is the longest NBA game every played as of 2015. It clocked in at 78 minutes long, a full 30 minutes longer than the typical 48-minute game.