According to this article on c|net:
Two … users have now revealed functioning hard drives built inside Minecraft that can read and write data. The first, created by Reddit and Imgur user smellystring can store 1KB [sic] of data, while a second, larger unit created by The0JJ can store 4KB [sic] of data.
"One day we will build a full computer in Minecraft, then play Minecraft on it. then the universe will crash," writes Imgur user mkat10z. Turns out, someone has already done that, creating a 2D platformer version of Minecraft that you play within Minecraft on a redstone computer.
UPDATE: It appears the referenced article was in error; the actual capacities should be in kilobits.