2 Some basic formating of the quotes
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The human brain consists of about one billion neurons. Each neuron forms about 1,000 connections to other neurons, amounting to more than a trillion connections. If each neuron could only help store a single memory, running out of space would be a problem. You might have only a few gigabytes of storage space, similar to the space in an iPod or a USB flash drive. Yet neurons combine so that each one helps with many memories at a time, exponentially increasing the brain’s memory storage capacity to something closer to around 2.5 petabytes (or a million gigabytes). For comparison, if your brain worked like a digital video recorder in a television, 2.5 petabytes would be enough to hold three million hours of TV shows. You would have to leave the TV running continuously for more than 300 years to use up all that storage.

From: http://www.scientificamerican.com/article.cfm?id=what-is-the-memory-capacity "The human brain consists of about one billion neurons. Each neuron forms about 1,000 connections to other neurons, amounting to more than a trillion connections. If each neuron could only help store a single memory, running out of space would be a problem. You might have only a few gigabytes of storage space, similar to the space in an iPod or a USB flash drive. Yet neurons combine so that each one helps with many memories at a time, exponentially increasing the brain’s memory storage capacity to something closer to around 2.5 petabytes (or a million gigabytes). For comparison, if your brain worked like a digital video recorder in a television, 2.5 petabytes would be enough to hold three million hours of TV shows. You would have to leave the TV running continuously for more than 300 years to use up all that storage."

The brain has about 100 billion nerve cells, so at least that many bits (about 10 gigabytes) could be stored, assuming the brain uses binary logic. But it probably doesn't do so. Instead, information is believed to be stored in the many connections that form between the cells. This is a much larger number: Current estimates of brain capacity range from 1 to 1000 terabytes! It would take 1,000 to 10,000 typical disk drives to store that much information.

From: http://www.moah.org/exhibits/archives/brains/technology.html "The brain has about 100 billion nerve cells, so at least that many bits (about 10 gigabytes) could be stored, assuming the brain uses binary logic. But it probably doesn't do so. Instead, information is believed to be stored in the many connections that form between the cells. This is a much larger number: Current estimates of brain capacity range from 1 to 1000 terabytes! It would take 1,000 to 10,000 typical disk drives to store that much information. "

http://www.scientificamerican.com/article.cfm?id=what-is-the-memory-capacity "The human brain consists of about one billion neurons. Each neuron forms about 1,000 connections to other neurons, amounting to more than a trillion connections. If each neuron could only help store a single memory, running out of space would be a problem. You might have only a few gigabytes of storage space, similar to the space in an iPod or a USB flash drive. Yet neurons combine so that each one helps with many memories at a time, exponentially increasing the brain’s memory storage capacity to something closer to around 2.5 petabytes (or a million gigabytes). For comparison, if your brain worked like a digital video recorder in a television, 2.5 petabytes would be enough to hold three million hours of TV shows. You would have to leave the TV running continuously for more than 300 years to use up all that storage."

http://www.moah.org/exhibits/archives/brains/technology.html "The brain has about 100 billion nerve cells, so at least that many bits (about 10 gigabytes) could be stored, assuming the brain uses binary logic. But it probably doesn't do so. Instead, information is believed to be stored in the many connections that form between the cells. This is a much larger number: Current estimates of brain capacity range from 1 to 1000 terabytes! It would take 1,000 to 10,000 typical disk drives to store that much information. "

The human brain consists of about one billion neurons. Each neuron forms about 1,000 connections to other neurons, amounting to more than a trillion connections. If each neuron could only help store a single memory, running out of space would be a problem. You might have only a few gigabytes of storage space, similar to the space in an iPod or a USB flash drive. Yet neurons combine so that each one helps with many memories at a time, exponentially increasing the brain’s memory storage capacity to something closer to around 2.5 petabytes (or a million gigabytes). For comparison, if your brain worked like a digital video recorder in a television, 2.5 petabytes would be enough to hold three million hours of TV shows. You would have to leave the TV running continuously for more than 300 years to use up all that storage.

From: http://www.scientificamerican.com/article.cfm?id=what-is-the-memory-capacity

The brain has about 100 billion nerve cells, so at least that many bits (about 10 gigabytes) could be stored, assuming the brain uses binary logic. But it probably doesn't do so. Instead, information is believed to be stored in the many connections that form between the cells. This is a much larger number: Current estimates of brain capacity range from 1 to 1000 terabytes! It would take 1,000 to 10,000 typical disk drives to store that much information.

From: http://www.moah.org/exhibits/archives/brains/technology.html

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http://www.scientificamerican.com/article.cfm?id=what-is-the-memory-capacity "The human brain consists of about one billion neurons. Each neuron forms about 1,000 connections to other neurons, amounting to more than a trillion connections. If each neuron could only help store a single memory, running out of space would be a problem. You might have only a few gigabytes of storage space, similar to the space in an iPod or a USB flash drive. Yet neurons combine so that each one helps with many memories at a time, exponentially increasing the brain’s memory storage capacity to something closer to around 2.5 petabytes (or a million gigabytes). For comparison, if your brain worked like a digital video recorder in a television, 2.5 petabytes would be enough to hold three million hours of TV shows. You would have to leave the TV running continuously for more than 300 years to use up all that storage."

I'm no medical expert by any means, but according to this, roughly 2.5 petabytes. This seemed a little high so i looked some more.

http://www.moah.org/exhibits/archives/brains/technology.html "The brain has about 100 billion nerve cells, so at least that many bits (about 10 gigabytes) could be stored, assuming the brain uses binary logic. But it probably doesn't do so. Instead, information is believed to be stored in the many connections that form between the cells. This is a much larger number: Current estimates of brain capacity range from 1 to 1000 terabytes! It would take 1,000 to 10,000 typical disk drives to store that much information. "

This second article explains that if the brain used binary storage then it would be 1-10 terabytes, most likely around 3. But since the brain does not and it stores information in the connections it is much likely a lot more. But this article was written in 2000 I think.

The first article is on the high side, while the second article is on the more realistic side. But the truth is that no one knows because with the technology that we have and understanding of the brain it is impossible to accurately calculate this. from other sources that I have read it looks like between 3-100 terabytes is what is generally accepted. This is a large range, but because we don't know exactly. And a lot of the calculations assume things that we, as of right now, cannot be 100% certain on.

http://www.slate.com/articles/health_and_science/explainer/2012/04/north_korea_s_2_mb_of_knowledge_taunt_how_many_megabytes_does_the_human_brain_hold_.html was another good article.