The search for neutrinoless double-beta decay (0 nu beta beta) requires extremely low background and a good understanding of their sources and their influence on the rate in the region of parameter space relevant to the 0 nu beta beta signal. We report on studies of various beta and gamma backgrounds in the liquid-xenon-based EXO-200 0 nu beta beta experiment. With this work we try to better understand the location and strength of specific background sources and compare the conclusions to radioassay results taken before and during detector construction. Finally, we discuss the implications of these studies for EXO-200 as well as for the next-generation, tonne-scale nEXO detector.