My preliminary investigation for the Martingale Expectation system didn't reveal much good data. Although it is still a small sample size (only the Eastern Conference in the 2008-2009 season) I already have seen streaks of length 9, 10, 11.
Here is a graph of 1 game streaks. The data is arranged with the team with the highest record on the left (the Cavaliers) and the worst record on the right (the Wizards). This is the only interesting graph I've produced so far.