Human beings have the potential to develop a sense of humor and each is born with the capacity to laugh. (Padus, Emrika, et al. The Complete Guide to Your Emotions & Your Health. p 546-547. PA: Rodale Press, 1992.)

Damage to the right frontal lobe of the cerebrum can decrease one’s ability to appreciate humor. This can, in turn, reduce one’s tendency to smile or laugh in response to a joke. (Richard, MD. The New Brain. p 93-94. PA: Rodale, 2003.)

Humor and laughter are processed via a complex pathway of brain activity. Three main components: sections of the frontal lobe near the forehead to “get” the humor; the supplementary motor area for smiling / laughing muscle movements; nucleus accumbens to elicit happiness felt after a funny experience. (Humor, Laughter, and the Brain. Brain Briefings, December 2001. 
http://www.sfn.org/index.cfm?pagename=brainBriefings_humorLaughterAndTheBrain

Study 2003, Reiss and colleagues: the brain's mesolimbic reward center, which is responsible for the rewarding feelings that follow such events as monetary gain or cocaine use, is also activated by humor. (http://www.news-medical.net/?id=14460)

MRI study of brains of 16 healthy adults: used to detect areas of the brain that were activated when the subject found a cartoon funny. In addition to activating areas of the brain involved in language processing, humor also stimulated regions of the brain known as reward centers, such as the amygdala, which releases dopamine. (WebMD Medical News. Humor Activates Reward Center of the Brain. http://www.webmd.com/balance/news/20031203/funny-thing-about-humor-brain)

Study using EEG topographical brain mapping of an individual hearing a joke: left hemisphere began to process the words. Then the frontal lobe center of emotionality was activated. 120 milliseconds later the right hemisphere began processing the pattern. A few milliseconds later the occipital lobe showed increased activity. Delta waves increased, the brain got the joke, and laughter erupted. (Dunn, Joseph R., PhD, Ed. New Discoveries in Psychoneuroimmunology. p 6-7. (interview with Dr. Lee S. Berk).Humor & Health Letter, Vol III. No 6, Nov/Dec 1994, MS: Dunn.)

When using or experiencing positive humor and mirthful laughter, the whole brain is involved, not just one side, and there's more coordination between both sides. (O’Donnell, Sinara Stull. Laugh More at Work To Ease Office Stress. 
http://www.careerjournal.com/myc/climbing/20011206-odonnell.html)

fMRI Studies of brain activities activates in two types of humor. High-level visual areas were activated during visual humor and classic language areas were activated during language-dependent humor. (Watson, Karli K., et al. Brain Activation during Sight Gags and Language-Dependent Humor. 
http://cercor.oxfordjournals.org/cgi/content/abstract/bhj149v1)

Both hemispheres are needed to produce a fully rounded sense of humor. The left brain creates the feeling of amusement and so is quite happy to laugh at more or less anything when prompted to do so. The right hemisphere “gets” the joke by registering the dislocation in logic that is a hallmark of most formal humor. Meaning emerges from the pulling together of all the threads of the joke, including context, assumptions, and knowledge of personal prejudices. (Carter, Rita, Ed. Mapping the Mind. p 17. CA: University of California Press, 1998.)

The two hemispheres understand humor in two different ways. It takes a whole brain to appreciate a joke fully. The left is literal in its interpretations of the joke and is especially drawn to wordplay (e.g., the bigger the summer vacation, the harder the fall). The right is more alert to subtleties and nuances. (Wonder, Jacquelyn, and Priscilla Donovan. Whole Brain Thinking. p 105. NY: Ballantine Books, 1984.)

Humor processing (getting the joke and laughing) appears to involve parts of the frontal lobes and a component of the pleasure pathway, the anterior cortex of the hypothalamus. (Restak, Richard, MD. The New Brain. p 92-94. PA: Rodale, 2003.)

Various portions of the brain work together to experience humor and laughter. Left hemisphere sets up the joke. Right hemisphere is involved in getting the joke. (Dossey, Larry, MD. Healing Beyond the Body. p 133-149. Boston: Shambhala Publications, Inc., 2001.)

The left cerebral hemisphere creates the feeling of amusement and laughs when prompted. The right hemisphere “gets” the joke. (Carter, Rita, Ed. Mapping the Mind. p 36-38. CA: University of California Press, 1998.)

Refer to Laughter - Humor and the Brain for additional information.