According to an article in Scientific American (here), published in April 2010, the data storage capacity of the human brain is around 2.5 petabytes. A petabyte, for those that have temporarily forgotten, is 10**15, or written another way, 1.0E15, or for those that just like to see all the zeros it is 1,000,000,000,000,000 bytes. That is around about 1,000 terabytes—for those that find it easier to boggle terabytes.
Yep. So once you fill your noggin up with 1.0E15 bytes worth of data it will be full.
Now. If only we had some way of knowing how much we already had stuffed away in there so we knew how much storage space we had left.
In fact the brain’s best trick is not how much data it can store, which you have to admit is pretty awesome, but its amazing ability to find and recall information. The brain can access information based on simultaneous or individual cues from sound (including speech/language), sight, smell, taste, and touch.