On the evening of November 8, 1895, Wilhelm Conrad Roentgen noticed an unusual glow emanating from a screen of barium platinocyanide in his laboratory, where he had been performing experiments to determine the nature of cathode ray emissions. The cathode ray tube, which sends a stream of electrons through a glass-enclosed vacuum, had recently played a key role in several notable experiments, including J.J. Thomsons's famous set in which he proved the existence and negative charge of the electron.
The screen's fluorescence surprised Roentgen, as it was located more than a foot away, and the range of the cathode ray had been established as less than four inches. Furthermore, he had shielded the tube with black carbon paper to prevent light escaping. Roentgen spent the next six weeks trying to determine what had caused the fluorescence, and his work resulted in the discovery of a new type of electromagnetic wave, which he named the X-ray due to its enigmatic nature. (For a more detailed history look at Alexi Assmus's excellent article Early History of X-rays or the NDT's History of Radiography.)
Further experiments revealed that x-rays are emitted when electrons in a cathode ray stimulate a metal anode, causing the emission of energy in the form of electromagnetic radiation. Like all forms of light, X-rays exist simultaneously as wave and particle. They can also penetrate many solids that normal light rays cannot. (More information on cathode ray tube X-rays can be found here, while Michael Fowler's Rays and Particles goes deeper into the physics of X-rays.)
Roentgen's first experiments with the X-ray involved developing photographs of various items, using X-rays to expose the film rather than visible light, in order to determine whether X-rays were capable of passing through solids of varying density.
The most informative of these X-ray photographs (named Roentgenograms in his honor) was taken when he had his wife place her hand between the X-ray source and the photographic. The bone and tissue of her hand absorbed varying amounts of the X-ray because of their different densities, and the resulting image showed dark lines corresponding to the bones of her finger, surrounded by a cloudy outline corresponding to her skin.
Roentgen was well aware of the enormous help this technology could offer in diagnosing and treating previously undetectable internal ailments. Within a year after he published his findings, X-ray photographs were being used to assist doctors performing surgery and on the battlefield to locate bullets in the bodies of wounded soldiers. The impact of X-rays on the medical field has only increased since then with the development of fluoroscopy, angiography, and tomography. (See Otha Linton's Medical Applications of X Rays for a detailed timeline, or the Radiology Database for case studies.)
While Roentgen (and later physicists Braggs and von Laue) attempted to solve the X-ray's many mysteries, husband-and-wife scientist team Pierre and Marie Curie were on the verge of discovering yet another form of penetrating radiation. Their experiments with uranium ore led to the discovery of the elements radium and polonium, and introduced the world to the phenomenon of radioactive decay, inaugurating the nuclear age.
The French scientist Antoine Henri Becquerel independently discovered radioactive emissions through his work with potassium uranyl sulfate, finding that, unlike X-rays, these rays were affected by a magnetic current and therefore must have a charge. (Hyperphysics has an excellent introduction to the principles of radioactivity, and biographies of the Curies and their contemporaries can be found here.)
Scientists soon learned that radiation was not the innocuous form of energy Roentgen had presumed it to be. Marie Curie contracted and died of pernicious anemia, probably because of radiation overexposure. She was just one of many early radiation scientists who paid dearly for only learning the hazards of these rays after a lifetime of exposure to them.
Doctors began to notice the side-effects of these new forms of radiation on the human body, and gradually so did their patients. The unchecked propagation of radiation therapy had concealed the very real dangers of unprotected exposure to radioactive substances until enough evidence accumulated: people really were being poisoned by this supposedly beneficial energy.
The widely publicized story of the Radium girls of Orange, New Jersey, who worked in a factory painting watches with glow-in-the-dark radium paint that was slowly poisoning them, brought about a turning point in public awareness of the dangers of exposure to radiation. The EPA was established in 1970, in part to oversee radiation protection policy.
Despite their potential for great harm, X-rays and other forms of radiation continue to play a crucial role in medical and experimental science. Thanks the development of sophisticated computer technology, it is now possible to combine thousands of 2D X-ray slices into a 3D image for greater accuracy in pinpointing the location of tumors, bone breaks, and other internal ailments of the human body.
X-rays are also widely used outside of the medical field: their smaller wavelength gives a higher resolution than visible light when used in microscopes, and has helped researchers paint a 3D figure of the living cell. (See this article on X-ray crystallography for more about how this works).
X-rays are also used extensively in industry to check for damage to structural integrity that's invisible to the naked eye, again with the help of sophisticated computer programs. It is a safe bet that for the next hundred years, X-rays will remain as important to human endeavors as they have been over the last hundred.