This three pound chunk of complex meat inside your head is composed of 100,000,000,000 neurons (those feisty little electric units that unite to make your brain.) These 100 billion neurons can connect to other neurons a few times or hundreds of times. Given the quantity of neurons - the quantity of connections is astronomical, equaling (according to Steven Pinker) more than the number of atoms in the known universe (hundreds of trillions of connections.)
Interestingly enough, babies (those little bundles of joy) have twice as many neurons as us (200 billion) and undergo a ridiculous amount of neural-cropping (exactly what it sounds like - other cells in the brain called glia (a name for various cells, not just one kind) eat up (phagocytes - name for cells that devour "debris") and recycle the energy, while some myelinate (oligodendroglial cells) the axons of neurons.) Eventually, they have as "few" as you and me.
The best thing about your brain is illustrated in this wonderful video I found on youtube (god bless the internet - which, as of 2009 (according to labnol.org is around 182 million) is less than .2 percent of the number of neurons you and I have) is plasticity. Watch this video and freak out.
In short, the brain does not stop changing. In fact, neuroscientists are discovering that the brain is more plastic than they even thought ten years ago. What does this plasticity mean (for those of you who didn't watch the video) it means a girl who has had half her brain removed (hemispherectomy) can function almost normally (probably, to assign a percentage to an abstract concept like "normal," she is probably around 70-90%.) She was young, this helped. Even though plasticity is great, were a 30 year old to have half of her brain cut out he would have much less functionality that Jody Miller (see video) achieved.
I'm taking some psychology classes this semester - I plant to do loads of writing about the brain (since it helps me to learn.) If you want to learn with me, your more than welcome. Neuroscience is possibly the single most important science of this generation. Alzheimer's, Parkinson's, and Stroke (disorders we're all familiar with) are incredibly prevalent, frighteningly so. Researching the brain not only provides insights into philosophical concepts like "the mind" and free will, it also may help us keep our brains healthier longer.