According to Wikipedia's random trivia (via Rob),
The theoretical capacity of a Boeing 747 filled with Blu-Ray discs is 595,520,000 Gigabytes, resulting in a 245,829 Gbit/s flight from New York to Los Angeles.
However, first reactions to this suggest that we should look deeper. Upon investigation, it appears that they grossly underestimated the potential throughput of a 747.
After some investigation (even considering the new 3TB 3.5" drives available) the best storage medium that we came up with is Western Digital's Scorpio Blue: 1TB 2.5" drives. Given the noted atypical height (12.5mm) and the remaining dimensions from Wikipedia, we came up with a volume of 87,400 cubic millimeters per hard drive. Blu-ray discs (1.2 mm thick and 120mm across) has a volume of 13,600 cubic millimeters and a maximum capacity of 50 GB, Wikipedia thinks that a 747 can hold 162 cubic meters. Well, that same volume can hold 1,854,000,000 gigabytes (1.8 exabytes) if they had used scorpio drives instead, given the 747 a rate of 765,326 gigabits per second instead. Granted, the packing density of boxes far exceeds that of cylinders.
Unfortunately, this brought up another important point; could the plane even take off if it was carrying this much weight? The best number we could find for a weight of a disc was .034 lbs, whereas a scorpio drive weighs .26 lbs. Wikipedia luckily helps us out again, providing enough information to figure out that a 747 can carry approximately 502,100 pounds. Luckily, the 747 can carry the weight of 1,930,000 scorpio drives at once, just over the 1,854,000 drives that would fit inside.