There are numerous studies that have taken place over the years quantifying the benefits that result from meditation.

Provided here are several links to studies or articles that produce the most interesting and clear results of what can be achieved through meditation:

http://www.hno.harvard.edu/gazette/2002/04.18/09-tummo.html
Advanced meditators are able to change their body’s metabolism, temperature and other vital signs under extreme physical conditions.

http://www.sciencedaily.com/releases/2005/11/051110215950.htm
"Meditation is known to alter resting brain patterns, suggesting long lasting brain changes, but a new study by researchers from Yale, Harvard, Massachusetts General Hospital, and the Massachusetts Institute of Technology shows meditation also is associated with increased cortical thickness."

http://www.newscientist.com/article.ns?id=dn8317
"Meditating does more than just feel good and calm you down, it makes you perform better – and alters the structure of your brain, researchers have found.

People who meditate say the practice restores their energy, and some claim they need less sleep as a result. Many studies have reported that the brain works differently during meditation – brainwave patterns change and neuronal firing patterns synchronize."

http://www.news.wisc.edu/13890
"For hundreds of years, Tibetan monks and other religious people have used meditation to calm the mind and improve concentration. This week, a new study shows exactly how one common type of meditation affects the brain.

Using a scanner that reveals which parts of the brain are active at any given moment, the researchers found that meditation increased activity in the brain regions used for paying attention and making decisions."

http://psyphz.psych.wisc.edu/web/News/NYT_Med_0507.html

NYTimes.com - Study Suggests Meditation Can Help Train Attention

"In meditation, people sit quietly and concentrate on their breath. As air swooshes in and out of their nostrils, they attend to each sensation. As unbidden thoughts flutter to mind, they let them go. Breathe. Let go. Breathe. Let go.

According to a study published today in the online edition of the journal PloS Biology, three months of rigorous training in this kind of meditation leads to a profound shift in how the brain allocates attention. "