Historical examples of arms races abound. One significant recent example was the competition between the Soviet Union and the United States to develop improved, and more, nuclear weapons during the Cold War. Carl Sagan once famously described this arms race with the analogy of "two men standing waist deep in gasoline; one with three matches, the other with five."
The term 'arms race' is also used generically to describe any competition where there is no absolute goal, only the relative goal of staying ahead of the other competitors. "Evolutionary arms races" are common occurrences in evolution theory, for example predators evolving more effective means to catch prey while their prey evolves more effective means of evasion.