Although the nucleus accumbens, in the limbic system near the center of the brain, is usually considered the "pleasure center" of the brain, but this is actually a misnomer, as the brain has multiple pleasure centers. However, the nucleus accumbens is the among the most prominent.
The nucleus accumbens mediates the release of the neurotransmitter dopamine, which underlies pleasure and relaxation. But the dopamine itself is released from the ventral tegmental area (VTA), another contender for the title of "pleasure center." The VTA releases dopamine to the nucleus accumbens, the prefrontal cortex, amygdala, and septum, all of which play an important role in what is called the reward circuit.
The term "pleasure center" originated with experiments by James Olds and Peter Milner in the 1950s probing the limbic systems of rats. They found that the rats quite enjoyed stimulation of their septal areas, located near the brain stem and among the oldest areas of the brain. In fact, the rats enjoyed it so much that they would cross highly electrified floors to reach a switch that stimulated it, and would press that switch thousands of times at the exclusion of all else. Female rats would even abandon their unweaned pups to self-stimulate their pleasure center.
Only a few experiments have been conducted involving the electrical stimulation of human pleasure centers. Generally these investigations are considered taboo. In the 1970s, Dr. Robert Heath, who believed he could "cure" homosexuality, wired up gay volunteers to an electrical apparatus that directly stimulated their nucleus accumbens, producing feelings of extreme pleasure. Given the choice, one man, code-named B-19, electrically self-stimulated his reward circuitry some 1,500 times. Few experiments directly stimulating the human pleasure centers have been conducted since.
It is interesting that the pleasure centers and the reward circuit are among the oldest areas of the brain. This means they were the first to evolve, and underscores the fundamental nature of pleasure/pain centers as an evolutionary adaptation.