One can say "step forward" or "step forwards" with equal correctness, although forward is more often used. Only forward can be used to apply to a following noun: one can say "a forward movement" but hardly "a forwards movement." Forward is also preferred in such constructions as "bring forward," "come forward," and "from this day forward." As a verb, one can use only forward: "Please forward my mail to me." Since forward is never incorrect, why not always use it in preference to forwards? See also foreword.
Dictionary of problem words and expressions. Harry Shaw. 1975.