In order to better understand the forces that hold nuclei together, one hopes to study as many different nuclei as possible. Nuclides are found naturally up to Z=94. Everything higher than Z=83 (bismuth) is radioactive.
Two elements, technetium (Z=43) and promethium (Z=61) are entirely synthetic -- there are no known natural sources.
After Word War II, there has been steady interest in making new elements. Some of these even have found commercial uses, Americium-241 (Z=95) is used in some home smoke detectors, for example.
Nuclear scientists have predicted that some elements in the region of Z=114 would show special stability.