For as ubiquitous a word as "dude" is, etymologists don't actually know how or where it started. But that hasn't stopped them from suggesting a wide array of possibilities.
And the suggestions aren't of the flattering kind. They range from dude being an abbreviation for "dudenkop," the German word for "blockhead," to it being the favored greeting between New York dandies—"How dew you dew?"—to it being the result of a poor British pronunciation. Oxford Etymologist, Anatoly Liberman, also points to an 1895 Thomas Hardy novel as a potential source. The novel used the term as a facetious slang for overdressed pretty-boys and attributed it to a contemporary American businessman, Hermann Oelrichs.
But despite the numerous hypotheses, the world may never know the origin of the most versatile word in the English language (case in point: Dude, Where's My Car?). According to Liberman, "Monosyllables beginning and ending with b, d, g (and even with p, t, k) are the dregs of etymology." [Oxford Etymologist via Braniac]