Dr. Manhattan controls matter. This gives him the ability to teleport himself and others great distances, alter his size, alter elements, project himself or his mind telekinetically, create clones of himself and exist in the past, present and future at once.
Jonathan Osterman was a promising scientist at the Gila Flats Research Center in Arizona before a tragic accident involving the removal of his intrinsic field destroyed his body, splitting him into his constituent atoms. Somehow Osterman managed to restructure himself as a humanoid being and returned to our plane. He brought with him the power to control matter.
Realizing this incredible being had applications in the military and space divisions, the United States government took Jon into it's folds, and gave him a codename meant to strike fear into America's enemies, a name associated with America's power: Dr. Manhattan.
The U.S sent their new soldier into battle. In the 1970's, Dr. Manhattan was almost solely responsible for ending the Vietnam war. He continued to live under government supervision, performing various tasks, and continuing his own research. With his ability to generate elements, Dr. Manhattan developed numerous inventions, including the electric car, making the gas-powered car obselete.
After leaving the Earth due to a cancer scare, Dr. Manhattan returned too late to prevent Adrian Veidt's New York massacre. After realizing he was morally in checkmate, Dr. Manhattan left for a far away galaxy, claiming he was going to create human life. He had evolved into a near God-like state.
DR. MANHATTAN'S QUOTES:
"The end? Nothing ends, Adrian. Nothing ever ends..."
"There is no future. There is no past. Do you see? Time is simultaneous, an intricately structured jewel that humans insist on viewing one edge at a time, when the whole design is visible in every facet..."