The Chinese system uses fire, water, metal (gold), earth and wood; these are also planet names and days of the week (carried over also into Japanese, although the classical Japanese elements follow the South Asian pattern below). Traditional Chinese science treats these slightly differently from Western science; rather than being foundational building blocks, each "element" has characteristics that indicate changes in states that are fundamental. Needham's Science and Civilisation in China has a good summary of this system.

Many other elemental systems, however, follow the same pattern as those from Classical antiquity - earth, wind, fire, water. Some add "void" or "space" to this but not all.

Worth noting, of course, that (although this is a massive oversimplification) Democritus and Leucippus were proponents of atomic theory in classical antiquity, even if they were still some way off the mark.